For simplicity, I just did it directly using standard base 10 Logs. 3XLog2=(2-X)Log7. 3XLog2=2Log7-XLog7. 3Xlog2+XLog7=2Log7. X(3Log2+Log7)=2Log7. X=2log7/(3log2+Log7). From calculator, X= 0.9668274. All good from you,thanks😊
@@KasyannoEZMath I did it a very similar way, and it is worth pointing out your final answer is a bit off, probably because you did some of the final arithmetic with pre-rounded numbers. I got the same answer to 8 decimals as Monty., and plugged it back into the original equation, and it was correct.
James Nicholson, thanks for your time. About the list you're asking about, please be specific. Solving an exponential equation is a complex task and involves lots of incorporated math concepts to solve a single problem. Have a great day!
@@jamesnicholson2503, thanks for your determination to learn. First, in solving exponential equations, the full knowledge and understanding and the skills to apply the exponent rules and the logarithm rules are vital. The full understanding of the logarithms is what you need, aside from the exponent rules, since logarithms is the inverse of exponent. This means, to undo an exponent you need to use the rules of logarithms. Second, the full knowledge on algebra solving equations and skills are the basic foundation. I hope that this can help you in any way in your journey to learning how to solve exponential equations. Keep up the good work, you are on the right track. Have a great day!
For simplicity, I just did it directly using standard base 10 Logs.
3XLog2=(2-X)Log7.
3XLog2=2Log7-XLog7.
3Xlog2+XLog7=2Log7.
X(3Log2+Log7)=2Log7.
X=2log7/(3log2+Log7).
From calculator,
X= 0.9668274.
All good from you,thanks😊
Monty North, you're awesome! Thanks for your time commenting on this video. Have a great day!
@@KasyannoEZMath I did it a very similar way, and it is worth pointing out your final answer is a bit off, probably because you did some of the final arithmetic with pre-rounded numbers. I got the same answer to 8 decimals as Monty., and plugged it back into the original equation, and it was correct.
@@fraserorr,you're awesome! You're right on that. Rounding off of numbers would make a big difference. Thanks for your time. Cheers 🍻!
Logªb-c ≠ Logªb - Logªc
I used the method of direct substitution to check the answer - this is solving problem without paper and pencil.
That's brilliant!. Thanks for your time. Have a great day!
Thanks.
You're welcome!
Solving Exponential Equation: 2^3x = 7^(2 - x)
Convert the exponential base number from 2 to 7 or vise versa, whichever is easier:
Let 7^n = 2, n = log2/log7 = 0.301/0.845 = 0356; 7^0.356 = 2
2^3x = (7^0.356)^3x = 7^[(0.356)(3x)] = 7^1.068x = 7^(2 - x)
1.068x = 2 - x, 2.068x = 2; x = 2/2.068 = 0.967
Answer check:
2^(3^x) = 2^[(3)(0.967)] = 2^2.901 = 7.469
7^(2 - x) = 7^(2 - 0.967) = 7^1.033 = 7.464; Confirmed
@Walter Wen, you're awesome! That's a nice solution. Thanks for your time, I appreciate it. Have a great day !
🙏
How is it worked out please, can some one do me a list,thank you.
James Nicholson, thanks for your time. About the list you're asking about, please be specific. Solving an exponential equation is a complex task and involves lots of incorporated math concepts to solve a single problem. Have a great day!
@@KasyannoEZMath Yes,but please tell me roughy how its worked out,thank you!
@@jamesnicholson2503, thanks for your determination to learn. First, in solving exponential equations, the full knowledge and understanding and the skills to apply the exponent rules and the logarithm rules are vital. The full understanding of the logarithms is what you need, aside from the exponent rules, since logarithms is the inverse of exponent. This means, to undo an exponent you need to use the rules of logarithms. Second, the full knowledge on algebra solving equations and skills are the basic foundation. I hope that this can help you in any way in your journey to learning how to solve exponential equations. Keep up the good work, you are on the right track. Have a great day!
Very informative. Well done
Thanks a lot, chris! Have a great day!
@@KasyannoEZMathI especially like how detailed the explanations were. They're perfect for opsimaths like me.
@chris thanks for liking the way I do. It's never too late to learn anything that you would like to learn or relearn. Have a great day!
By looking the equation without writing the solution or using log. The answer is more than 0 and less than 1.
Teogilo Daquipil, you're right on that. Some problems posted have their answers be readily calculated. Thanks for your time. Have a great day!
Thanks!
You're very welcome, Dushyantha Bandara! Have a great day!
2ln7/(3ln2 + ln7)
Pradeep Sahoo, you nailed it! That's awesome! Thanks for your time. Have a great day!
Thank you for the video.
You're very welcome, George! Have a wonderful day!
You're very welcome, George! Have a great day!
ln of both sides. The rest is cake.
You're awesome, jim! 🍻!
I found 0.947 - NOT too far away and did this in 10 seconds 😁
👍
I thought it was 1 but it turned out to be 7
Yup! It's 7. Thanks!
Just take the log right away and it’s a simple solution x=2log7/(3log2+log7) in less than a minute
@@JL-zt3tu that's perfect! Cheers 🍻!
==Daiktas Lygus {{{2^3x=2^[7-3,5x]= [3x= 7-3,5x]=[ 6,5x=7]=[ x= 7-6,5 = 7/6,5= 0,5
marcelius, you need to redo your solution. Thanks!
0.9668273972354 is the value of x solved with computer with regression.
this is easiter to solve with computers than with humans.
equus, that's awesome accuracy to13 decimal places solved by computer! Thanks for your time, sir. Have a great day!