A tricky math problem for 9th Graders | Can you solve?

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[@NeveraDalmatica]

That a ninth grader can solve this equation is just as likely as the same ninth grader being able to solve a partial differential equation.😄

[@DanielSong39]

Looks like a math contest problem for ninth graders

[@Segalmed]

8^x = (2^x)³ . Substitute a for 2^x => a³ + a = 30. That ones is easy to guess: a=3 (27+3=30).
=> 2^x = 3 => x*ln(2)=ln(3) => x= ln(3)/ln(2)

[@firstname4337]

so you watched the video just like everyone else

[@Segalmed]

@@firstname4337 nope

[@SmartGuyz]

(27+2=30) should be (27+3=30) in this case

[@Segalmed]

@@SmartGuyz Thank you!.
I have corrected the typo now.

[@justinstephenson9360]

A step was missed.
Once you get to 2^x=3
Take a natural log on both sides you get log2^x=log 3
Basic rule of logs is log a^b=b.log a
=>log 2^x=x.log 2 substitute that back into the equation gives you x.log2=log 3
=>x=log 3/log 2
On basis it is a 9th grader question and therefore complex roots are unlikely to be asked for, once you get to y(y^2+1)=30 it is relatively easy to see that y=3 is one answer because the integer factors of 30 are 3,10 or 5,6 (or vice versa) and we know that y30 when y>=6. That does not mean it is the only answer hence the wonderful extra steps in the video

[@pennstatefan]

Take the natural log of both sides, ln( 8^x + 2^x) = ln30. One then has x*ln2 + xln8 = ln30. x = ln30/(ln2 + ln8).

[@964tractorboy]

I really enjoy your solutions to these problems. Thanks for sharing.

[@engone6380]

I thought about the same. Substitute 2^x by a for example, then write as follow a^3+a=30 then a(a^2+1)=30= 3(3^2+1).... Then a eq 3, much easier

[@Gnowop3]

In the old days when there was no calculator, we use log (base 10) because we have to use a look up table. In 2024, we can get results from calculator of different bases. Therefore 2^x = 3 => x = log3(base 2) [by definition]. Just find the value of x directly from the calculator without doing log3/log2.

[@dinabandhusaha5520]

Thank you for this

[@rrraewr]

Lol i guesstimated it at 1.6 because 8 to the power of 1.5 is 8*2+ less than 8, which nets you close to 24, so some has to be missing to reach 30 with the help of 2 to not entirely the power of 2, has to be a step above 1.5, meaning 1.6

[@better_than_uNOOB]

u make very good videos i am in 8th and love loearning from u

[@yanssala2214]

X = ln 3 / ln 2 = 1,58496..... # irracional el truco es un cambio de variable u = 2^x que conduce a una ecuacion simple de tercer grado u^3+u=30 una de sus soluciones es u = 3. Luego aplicar propiedades de los logaritmos y listo. Xln2 = ln 3 y ya sabemos el final.

[@jdcunnington]

I've forgotten something. At 6:02, how does the last (y-3) become 1? There's something I missed.

[@himanshusekharsahoo7301]

He took (y-3) common.

[@jdcunnington]

@@himanshusekharsahoo7301 - oh, of course.

[@Unbathed]

(I was in ninth grade 56 years ago. )
I tried to find the answer here starting with 30 = 2^5 - 2^1 followed by …
2^2X + 2^(X-1) = 2^4 - 1
… and got nowhere.
Thank you for the rescue

[@nathanw4018]

You could also graph both sides of the equation and have a close approximation in 60 seconds

[@RealQinnMalloryu4]

8^3x+2^3x={24x^3+6x^3}=30x^6 24^6x^6 2^12^2^3x2^3 1^6^1^1x1^1 3^2x^1^1 3^2x(x ➖ 3x+2).

[@engone6380]

I thought about the same. Substitute 2^x by a for example, then write as follow a^3+a=30 then a(a^2+1)=30= 3(3^2+1).... Then a eq 3, much easier

[@richardl6751]

@@engone6380 He's not actually doing anything.

[@sunilramkarran7037]

You have to talk more slow