(3 to the m) - (2 to the m) = 65 m=? MOST won’t FIGURE OUT how to solve!

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  • Опубліковано 30 січ 2025

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  • @tomtke7351
    @tomtke7351 Місяць тому +8

    3^m - 2^m =65
    stumble around
    m=5 =>
    3^5-2^5=?65
    81×3-16×4=?65
    243-64=?65
    179 /=65
    m=4
    3^4-2^4=?65
    81-16=?65
    65=❤65✔️
    3^m-2^m=65
    ÷2^m{3^m-2^m=65}
    (3^m/2^m) - 1 = 65/2^m
    1.5^m - 1 = 65/2^m
    1.5^m - 65/2^m = 1
    X^2 - Y^2 = (X + Y)(X - Y)??

  • @dericcadora2801
    @dericcadora2801 25 днів тому +16

    All you did was basically solve it via trial and error in a complicated way. Kind of a dud here

    • @jimmacaulay844
      @jimmacaulay844 13 днів тому +1

      Not true, he ended up solving it analytically.

    • @WayneSalhany
      @WayneSalhany 6 днів тому

      He needs to show firstly that exact methods are inadequate and then transition to successive approximation. By ignoring of avoiding the subject he is ?? IDK.

  • @robertjohnson4401
    @robertjohnson4401 Місяць тому +4

    At exactly 16 minutes into the video, recognize that 65 is equal to 13 x 5. This simplifies the calculation to arrive at a=9. Set a+b=13, a-b=5. Therefore, a=9, b=4.

  • @jimselvy6157
    @jimselvy6157 25 днів тому +11

    Like most of his videos, lots of unnecessary babbling, with too many tangents. This ends up not being an algebra problem, just trial and error. His trial and error is more complicated than using original equation.

  • @richardmullins44
    @richardmullins44 18 днів тому +2

    by inspection, 3^4 - 2^4 = 81 - 16 = 65

  • @russelllomando8460
    @russelllomando8460 Місяць тому +5

    thanks for the lesson

  • @armchairtin-kicker503
    @armchairtin-kicker503 Місяць тому +6

    Here's the last half of the solution, employing a system of linear equations.
    .
    let a = 3^(m/2) and b = 2^(m/2)
    a^2 - b^2 = 65
    (a - b)(a+b) = 65
    Factoring 65...
    (a-b)(a+b) = 5*13
    a - b = 5 [equ. #1]
    a + b = 13 [equ. #2]
    2a = 18 [equ. #1 plus equ. #2]
    a = 9
    Back substituting the value 9 for variable-a...
    (9) = 3^(m/2)
    3^2 = 3^(m/2)
    log(3^2) = log(3^(m/2))
    2log3 = (m/2)log3
    2 = m/2
    4 = m
    m = 4
    Therefore, m is equal to 4.

    • @Dr_piFrog
      @Dr_piFrog Місяць тому +4

      This is the proper solution, not the round-robin third treatment presented in the video.👍

    • @Emadagban777
      @Emadagban777 5 днів тому +1

      How would you solve such problem problems when m is an odd number?

  • @rfarrelldic
    @rfarrelldic Місяць тому +3

    solution number three is innovative but it is really trial and error again .... and if we are going to sell by trial and error error, it's much easier to just do it out right with the original equation

  • @johnlakin5895
    @johnlakin5895 Місяць тому +4

    Nope…that one was beyond me.

  • @Kleermaker1000
    @Kleermaker1000 Місяць тому +4

    This is just the same as 81 - 16 = 65 and then transform 81 into 3^m (or 3^4) and 16 into 2^m (or 2^4). This is no real algebra imho, even though m = 4.

  • @conniebartley4226
    @conniebartley4226 23 дні тому

    I was really good at Algebra but this one is beyond my understanding. Graphing seems to be the best way to solve the problem.

  • @terry_willis
    @terry_willis Місяць тому +1

    This problem should be in the Math Olympiad.

    • @LPvsHH
      @LPvsHH Місяць тому

      Well it was. I typed the problem and saw titles like "Math Olympiad (3^m) - (2^m) = 65". So probably he took the problem from that Olympiad.

    • @CrYou575
      @CrYou575 14 днів тому

      Looks way too simple for that.

  • @marcoalby7499
    @marcoalby7499 22 дні тому

    Tecnica dell'avvicinamento graduale: 3 * - 2 * = 65 ... dove * = m, a = 3 * , b= 2 * --> ci sono solo 3 possibilità, 1 per ogni diverso valore di * : (a - b) < 65 , (a - b) = 65, (a - b) > 65
    si procede per tentativi: 1) * = 3 --> 27 - 8 = 19 19 243 - 32 = 211 211>> 65 3) * = 4 --> 81 - 16 = 65 65 = 65 confermato, m = 4 (Marco Alby)

  • @kajamix
    @kajamix 17 днів тому

    The simplest solution is this: First m = 4 is a solution, by trial and error. Then 3^m - 2^m = 3^m . (1 - (2/3)^m) and this is obviously an increasing function. So for m > 4, 3^m - 2^m is > 65.
    So there is no other solution.

  • @valentin5403
    @valentin5403 19 днів тому +1

    No one said why m=4 is the ONLY solution

  • @pedrojose392
    @pedrojose392 18 днів тому

    You have to find x so that:
    g(x)=3^m=65+2^m
    If m>=0 then both g(m) and f(m) are monotonocies funciona.
    But g(m) grows faster than f(m)
    As f(0)=66>1;g(m)=f(m) for some m* and after that as g(m) grows faster than f(m), g(m)>f(m) for m>x*.
    Só m* is unique for m>=0.
    for m

  • @gspaulsson
    @gspaulsson 21 день тому +1

    dunno how anyone else does it, but I generally start with a ballpark guess. 3^m >65, 3^4=81, 81-65=16= 2^4, problem solved. Any other possibilities? Negative? Fractional? Imaginary? Don't think so, but proofs would be interesting.

  • @roccov11
    @roccov11 17 днів тому +1

    OK, that's relatively easy to work out by trial and error, so how about solving this equation where the right hand side is 536.784 instead of 65. I know what m is because I chose a random figure to 3 decimal places and plugged it into the equation, but I'd like to see how you or anyone else solves this. I don't think I can.

    • @roccov11
      @roccov11 17 днів тому

      Using algebra I mean, not graphing. I could solve it by using an excel sheet and doing semi-manual iteration to home in on the answer.

  • @bobwilson3980
    @bobwilson3980 22 дні тому +1

    This is another arrow with the target drawn around it.

  • @andrespataky8410
    @andrespataky8410 10 днів тому

    Very nice solving but...was it luck? Can you find "m" in another similar exponential equation, or this was a special case?

  • @gregorynelson1568
    @gregorynelson1568 14 днів тому

    Through trial and error, m=4, but I was able to start with the observation that 3ᵐ > 65, and 3³- 27, while 3⁴=81, checking 4:
    3⁴ - 2⁴ = 81 - 16 = 65

  • @reinymichel
    @reinymichel 17 днів тому

    Twice at the beginning of your video you said 3m - 2m instead of "3 to the m minus 2 to the m"
    Secondly , at no point di you use a method other than "just trial and error" method, what if the equation had been 3^m - 2^m = 64 ?

  • @fernandocagarrinho3980
    @fernandocagarrinho3980 Місяць тому

    How about proving that m has to be even for the result to be a multiple of 5.
    And equating prime factors of 65=5*13 to solve the difference of squares.
    That would teach something.

  • @thomashawkinson7017
    @thomashawkinson7017 Місяць тому

    Roller coaster ride! Thanks.

  • @John-dp8oh
    @John-dp8oh 11 днів тому

    3^m must be greater tan 65 since 3^m-2^m is = 65. Try m =4, 3^4 =81; Subtract 2^4 =16 gives 65 so m=4.

  • @cyruschang1904
    @cyruschang1904 Місяць тому

    3^m - 2^m = 65
    3^4 - 2^4 = 81 - 16 = 56
    x = 4

  • @DennisMcFall
    @DennisMcFall Місяць тому +4

    Interesting but takes too long to get to the point/solution.

    • @jtinalexandria
      @jtinalexandria Місяць тому

      He goes off on too many tangents. Very distracting for kids with ADHD.

  • @wilgoster
    @wilgoster Місяць тому

    Nice, living in the universe of whole numbers.

  • @jaggisaram4914
    @jaggisaram4914 13 днів тому

    Ⓜ = 4 . 81- 16 = 16

  • @abdulhusseinalsultani9222
    @abdulhusseinalsultani9222 22 дні тому

    65 less and near 81=3^4 ie m=4
    81_16=65
    3^4_2^4=81_16=65

  • @Bill_Woo
    @Bill_Woo 21 день тому

    Why was negative 4 ignored?
    Okay, negative 5 as well?
    I suppose it'll be because you "deduced or induced" with the simple test what the solution must be, so you could just pick the simplest path that reached paydirt. But I still have an itch.

  • @Rich.Staples
    @Rich.Staples Місяць тому +1

    why not bring the whole equation to the (m/1) power? this would eliminate the variable power over 3 and -2 and put the 65 to the (m/1) power? u'd then end up with m=0

  • @tanveernaeem1157
    @tanveernaeem1157 25 днів тому

    Took less than 30 seconds. 3^4-2^4=65' m=4.

  • @mda7763
    @mda7763 9 днів тому

    Says I’m going to show you the answer in just a second then proceeds to talk about nothing for over a minute……..

  • @notreallydavid
    @notreallydavid Місяць тому

    'exacerbated at this'

  • @alexanderizhaki1560
    @alexanderizhaki1560 20 днів тому

    it is easy to guess : m=4, 81 -16

  • @rarocon
    @rarocon Місяць тому

    81 - 16 = 65 = 9² - 4² = 3² * 3² - 2² * 2² .. der Rest ist die Ausgangsaufgabe

  • @MrGfmassot
    @MrGfmassot Місяць тому

    Okay.... I guess that's how you do it.

  • @mehdizangiabadi-iw6tn
    @mehdizangiabadi-iw6tn Місяць тому

    e^x-√x/x=0

  • @vijaybhatia2686
    @vijaybhatia2686 Місяць тому +1

    What if the problem was 3*m + 2*m = 97 ?

    • @LPvsHH
      @LPvsHH Місяць тому +1

      It's 110% easier just combine like terms, and it becomes obvious: 3m+2m=97 5m=97 m=97/5 m=19.4

  • @mda7763
    @mda7763 9 днів тому

    Skip the first 7 minutes.

  • @Neil-e4n
    @Neil-e4n Місяць тому +1

    A little rant:
    It’s irksome that a lot of the comments read as;
    “It’s all about me, I’ve already learnt this stuff so you shouldn’t bother taking the time to try to help other people learn stuff I already know.”
    “I didn’t know something then I gained the knowledge and now it makes me feel good about myself to tell people, who haven’t gained the knowledge, how easy it is for me”,
    Have some humility.

    • @allenshallbetter
      @allenshallbetter Місяць тому

      You are right on. The ones making the negative remarks are, apparently, so knowledgeable in math; then why are they watching this? Let those who want to learn, watch and learn.

  • @syedfazlullah6459
    @syedfazlullah6459 Місяць тому

    You can solve this by trial and error method

    • @CrYou575
      @CrYou575 14 днів тому

      He basically did it that way.

  • @panlomito
    @panlomito Місяць тому +1

    I didn't know where to start but you can still try some numbers by estimation. So I started with 3^4 = 81... quite nice!
    81 - 65 = 16 = 2^4 and bingo !!!

  • @wes9627
    @wes9627 Місяць тому

    How about 3^m-2^m-64=0 or 3^m-2^m-66=0 or more generally f(m)=0 where m exists and is real? Iterative solution methods such as fixed-point or Newton-Raphson iteration may be used to approximate one or more values, if they exist. When m is presumed to be a posaiive integer a good place to start, since 3^m>2^m, is m=ceiling(ln65/ln3)=4, giving 3^4-2^4=81-16=65.

  • @sammymcclelland1071
    @sammymcclelland1071 10 днів тому

    M is 4

  • @roshanjain8374
    @roshanjain8374 19 днів тому

    No need to solve, answer is m=4.

  • @aajjuudyo
    @aajjuudyo 16 днів тому

    m= 5.

  • @melissalevine2373
    @melissalevine2373 23 дні тому

    I help students with math. It would be helpful if you would stay on subject a little better.

  • @josephlaura7387
    @josephlaura7387 Місяць тому +2

    Thank you

  • @AllDogsAreGoodDogs
    @AllDogsAreGoodDogs Місяць тому

    The answer is 4. M=4.

    • @discobear5752
      @discobear5752 Місяць тому

      Good dog! And hello from a fellow dog.

  • @sandeepsantoriya822
    @sandeepsantoriya822 16 днів тому

    कहना क्या चाहते हो😂
    One can solve it by hit and trial method
    Or by graphical method

  • @Majan-v8K
    @Majan-v8K Місяць тому

    m= 4

  • @ferrantepallas
    @ferrantepallas 25 днів тому

    4 .... 3 seconds

  • @mauriziograndi1750
    @mauriziograndi1750 Місяць тому +1

    3^4-2^4 = 65
    m = 4 no calculator.
    Or ln65/ln3 = 4.0 = m
    Perhaps not so academic but it works.

  • @meshulamoren8633
    @meshulamoren8633 22 дні тому +1

    הצבתי מיספרים עד שהיגעתי למיספר 4 .

  • @prpa9210
    @prpa9210 25 днів тому +2

    You take tooo long. You’re a typical ‘bad’ teacher - you love to hear yourself talk. Worst teacher, I feel sorry for your students!!!

  • @1234larry1
    @1234larry1 Місяць тому

    I found a crazy result of (a+b)=65 and (a-b)=1. The result is two values, one value for 3^m and another for 2^m
    The value for 3^m is m=2+2log 11{base3} and the value for 2^m is m=10, I checked them and they work, of course you’re supposed to have only one value for m across the whole equation, so that’s weird.

  • @aonghusobroin2959
    @aonghusobroin2959 Місяць тому

    4

  • @syedmdabid7191
    @syedmdabid7191 18 днів тому

    Id dicitur m= 4,respondeo😅😅😅😅😅😅🎉🎉🎉🎉❤😂

  • @holoparandeh4467
    @holoparandeh4467 Місяць тому +2

    sorry but you keep repeating yourself too often and prolonging your explanations .as a result one loses track , this should not have taken more than 6- 7 minutes.
    if someone doesn’t know 2 to the power 4 means 2x2x2x2 , should not even be trying to do this equation?!?!

  • @boonraypipatchol7295
    @boonraypipatchol7295 Місяць тому +2

    It is just one minute to solve this question,
    This vdo clip is 21 minutes,
    ..... What the babbling.....

  • @KHALEDMOFTAH-f8f
    @KHALEDMOFTAH-f8f 18 днів тому

    Too much repetition

  • @colwynbrennen
    @colwynbrennen 21 день тому +2

    Hey there, Mr. UA-cam Math Man! I've been really intrigued by this problem! Please note that for the duration of this post, I'm using x and y in place of a and b.
    As far as I can tell, you can only solve for the value of m using the difference of squares formula, x^2-y^2=(x+y)(x-y), when m is both a product of 2 and is greater than or equal to 2. In other words, an even number greater than or equal to 2. Thus, m can have a value of 2, 4, 6, 8, 10, 12, and so on. This is a direct result of the conditions established at the beginning of the problem by making x=3^(m/2) and y=2^(m/2). Therefore, m itself must always be a product of 2 in order to yield a whole number. For example, as seen in this problem, if m=4, then m/2=4/2=2. However, if m=3, you end up with the ratio m/2=3/2, which obviously doesn't yield a whole number when divided.
    Anyway, the value on the right side of the equation will need to change depending on the value of m so that the equation remains true. If m=4, we get 3^m-2^m=65, the equation used here. If m=2, the equation becomes 3^m-2^m=5. However, if m has a value that isn't a product of 2, you can't use the difference of squares formula to solve for it. Regardless of which pair of factors you use, you will end up with two numbers that can't be broken down into an exponent of either base 2 or 3. Even if you try using logarithms, you won't obtain the correct value for m. For example, when m=3, the equation becomes 3^m-2^m=19, which can't be solved using the difference of squares formula.
    However, it can be solved using the difference of cubes formula, where x^3-y^3=(x-y)(x^2+xy+y^2). In this case, the equation takes the form of x^3-y^3=19, where x=3^(m/3) and y=2^(m/3). However, just as using the difference of squares formula requires that m be a product of 2, so too does using the difference of cubes formula requires that m be a product of 3. In other words, m is both a product of 3 and is greater than or equal to 3. Thus, m can have a value of 3, 6, 9, 12, 15, 18, and so on. Once again, this is a direct result of the conditions established at the beginning of the problem by making x=3^(m/3) and y=2^(m/3). Therefore, m itself must always be a product of 3 in order to yield a whole number. For example, if m=3, then m/3=3/3=1. However, if m=4, you end up with the ratio m/3=4/3, which obviously doesn't yield a whole number when divided.
    Interestingly enough, just as using the difference of squares formula gives one set of (x,y) values, using the difference of cubes formula gives two sets of (x,y) values. In the case of x^3-y^3=19, where x=3^(m/3) and y=2^(m/3), one set of (x,y) values will be positive while the other will be negative. Obviously, only the positive set of (x,y) values will yield the correct solution.
    If m=6, the equation becomes 3^m-2^m=665. In this case, the value of m can be obtained by using either the difference of squares formula or the difference of cubes formula because 6 is evenly divisible by both 2 and 3. m/2=6/2=3 and m/3=6/3=2. For this reason, both formulas can be used when m has a value of 6, 12, 18, 24, 30, 36, and so on. This further implies that if m=4, you could also use x^4-y^4. If m=5, you would use x^5-y^5. If m=6, you could also use x^6-y^6, and so on. Obviously, using this approach will make your equations far more complex and not very practical each time the value of m increases. This also implies that using the difference of either squares or cubes won't solve for values of m which aren't evenly divisible by either 2 or 3, such as 5, 7, 11, 13, 17, 19, and so on. Also, things get kind of weird when m equals either 0 or 1.
    To sum up, use the difference of squares formula when m is a product of 2. Use the difference of cubes formula when m is a product of 3. And use either formula when m is a product of 6.
    Anyway, getting back to the original problem, when m is a product of 2, is greater than or equal to 2, and thus can be solved for using the difference of squares, only the middle pair of factors of the number on the right side of the equation will yield the correct solution. For example, if we take the equation presented in the video, 65 has four factors, which are 1, 5, 13, and 65. Only by using the two middle factors, 5 and 13, do we obtain the correct solution. Similarly, when m=8, the equation becomes 3^m-2^m=6305. 6305 has eight factors, which are 1, 5, 13, 65, 97, 485, 1261, and 6305. Once again, only by using the two middle factors, 65 and 97, do we obtain the correct solution. However, when m is a factor of 3, is greater than or equal to 3, and thus can be solved for using the difference of cubes, then it's possible for another pair of factors of the number on the right side of the equation to yield the correct solution instead of the middle two. This is especially true when m has a value of either 6 or 12. In any case, it's a process of rejection and elimination to find which set of factors gives the correct value of m. Finding the factors of any number is easy when using a website such as Number Empire.
    In addition to algebra, graphing is another ideal method for finding the value of m. If we use the equation presented here, 3^m-2^m=65, let m=x, then move everything to one side and make it equal to 0 or y, we get y=3^x-2^x-65. This produces a logarithmic graph with (x,y) intercepts at (4,0) and (0,-65). In other words, the graph intersects the y axis at -65 and the x axis at 4. If x=m, then 4 is our answer.
    For equations that prove difficult to solve using algebra, such as when m equals 0 or 1, equations involving the sum of squares, such as 2^m+3^m=13 when m=2, or when m is a value indivisible by either 2 or 3, such as when m equals 5, 7, or 11, then graphing is a viable, convenient, and useful alternative to find the value of m.
    Anyway, I would love to hear your thoughts on this! Or just graph it for fun! Either way, thanks so much for the content you post here on UA-cam! I find your discussions really entertaining! Keep up the good work, Mr. UA-cam Math Man!
    Grá ó Colwyn 🌝🦉🌲

  • @wallyb55232
    @wallyb55232 16 днів тому

    Why not take an hour? Add a few more smiley and sad faces and blah blah blah

  • @nikolaili1003
    @nikolaili1003 11 днів тому

    Teacher, you are talking too much...make it shorter...Hi from Croatia

  • @jas2819
    @jas2819 Місяць тому

    M=4. 🤗🤗 Way too easy. Me about 6 seconds.

  • @hankadelicflash
    @hankadelicflash Місяць тому

    The fact that this took almost 22 minutes to explain is why I hated math.

  • @syedfazlullah6459
    @syedfazlullah6459 Місяць тому

    Just put 4 in place of m

  • @billmorgan2883
    @billmorgan2883 Місяць тому

    This exact question has been done so many times before, why did you post this? You did exactly what the others posted with the exact amount of assumptions ie. "m" is a whole number. You could have at least tried factors of 1 and 65 and shown they did not work. At least it would have been slightly different from the other posts solving this exact same question. Or use the statement when factoring 65, we need prime factors. Just lazy content/math I think.

  • @BMT3691
    @BMT3691 18 днів тому

    Man!!!!! This is unwatchable,,,,,, so much extra extraneous nonsense information, instead of just getting to the F-ing point. This method of teaching is what made school difficult for some..

  • @shannonmcdonald7584
    @shannonmcdonald7584 Місяць тому

    I can look at it and tell u 4. But do you want all the imaginary solutions too?

  • @philfitter2408
    @philfitter2408 Місяць тому +1

    You love to talk talk talk. Get to the point. Not everyone has time on their hands as you 👎

  • @madradubh3127
    @madradubh3127 22 дні тому

    Talk too much....❤

  • @madurappankalyanaraman8015
    @madurappankalyanaraman8015 18 днів тому

    m=4 is the answer
    3⁴ -2⁴= 81-16=65

  • @valentin5403
    @valentin5403 19 днів тому +1

    4

  • @wilgoster
    @wilgoster Місяць тому

    Nice, living in the universe of whole numbers.

  • @samswift4921
    @samswift4921 Місяць тому

    M=4

  • @benbernard4058
    @benbernard4058 Місяць тому

    m=4

  • @engwj
    @engwj 11 днів тому

    4

  • @purushothamanmangalam7415
    @purushothamanmangalam7415 Місяць тому

    m=4

  • @syedfazlullah6459
    @syedfazlullah6459 Місяць тому

    m = 4

  • @venigallasatyanarayana9478
    @venigallasatyanarayana9478 20 днів тому

    m=4

  • @AllanPoeLover
    @AllanPoeLover 20 днів тому

    m = 4

  • @pas6295
    @pas6295 19 днів тому

    m=4

  • @Ajaykumar123_rcm
    @Ajaykumar123_rcm 11 днів тому

    M=4