A Fun Exponential Expression

Рет қаралды 18,007

Күн бұрын

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Пікірлер: 44

@moeberry8226 Жыл бұрын

In method 2 when you have 2^(a/b)=3 all you have to do is multiply both sides by 2 to obtain 2^(a+b)/(b)=6 then just cube both sides and that’s it.

@SyberMath Жыл бұрын

Nice!

@ezzatabdo5027 Жыл бұрын

Two nice solutions but the 2nd is more mentality... Too thanks Professor.

@SyberMath Жыл бұрын

Np. Thank you!

@noahvale2627 Жыл бұрын

Always a pleasure to watch and listen to you.

@SyberMath Жыл бұрын

Thank you!!! 🧡

@Victurf Жыл бұрын

Excellent!!!

@adamrussell658 Жыл бұрын

Take original equation and cube both sides you get 8^a = 27^b. Then multiply both sides by 8^b and you get 8^(a+b) = 216^b. Then take the bth root of both sides and you get 8^((a+b)/b)=216.

@ManjulaMathew-wb3zn 9 ай бұрын

3rd method Cube both sides then 8^a=27^b Multiply both sides by 8^b then 8^(a+b)=(8*27)^b Take bth root on both sides 8^(a+b)/b=8*27=216

@michaelbaum6796 Жыл бұрын

Nice video, thanks 👍

@SyberMath Жыл бұрын

No problem 👍

@duanephinney300 Жыл бұрын

Cube both sides, multiply by 8^b on both sides and take each side to the 1/b power and you get 27*8=216.

@alinayfeh4961 Жыл бұрын

nice work 👏

@SyberMath Жыл бұрын

Thanks

@devondevon4366 Жыл бұрын

yes, a fun problem 216 answer (2^a)^3 = (3^b)^3 cube both sdies 8^a = 27^b (8^a)^1/b = 27 raised both sides to the power of 1/b 8^a/b =27 (8^a/b) 8^1 = 27 x 8 multiply both sides by 8 8^a/b +1 = 216 rules of exponent (n^p * n^1 = n^P+1) a/b +1 = a/b + b/b = a+b/b hence 8^a+b/b = 216 answer

@KRYPTOS_K5 Жыл бұрын

Trick First method with ln To avoid the trap of to get a ln and the number 1 after division. If you can try to avoid 3 different types of things (ln, integers, variables). Reduce unknown things to recognize patterns.

@scottleung9587 Жыл бұрын

I took an approach similar to your second method.

@SyberMath Жыл бұрын

Excellent!

@antoniomastinu4700 Жыл бұрын

X=0!

@msathwik8729 Жыл бұрын

did Exactly second approach

@AdityaKumar-iy5pu Жыл бұрын

Same bro

@-basicmaths862 Жыл бұрын

a/b=log 3base2 Answer is 216, e^logx=x

@alextang4688 Жыл бұрын

A good question for school examination. 😋😋😋😋😋😋

@SyberMath Жыл бұрын

😊

@TheNarukman Жыл бұрын

I did the 2nd method the first time.

@vishalmishra3046 Жыл бұрын

a log 2 = b log 3 so a/b = log 3 / log 2 so (a/b+1) = (log 3 + log 2) / log 2 = log 6 / log 2 so (a/b+1) log 8 = (log 6 / log 2) x (3 log 2) = 3 log 6 = log 6^3 = log 216 Therefore, 8^((a+b)/b) = antilog ( log 216) ) = 216.

@abhitomar320 Жыл бұрын

Easy one

@MrGeorge1896 Жыл бұрын

I did a somewhat mixture of both methods 😄 and the same result 216.

@SyberMath Жыл бұрын

Nice work!

@calspace Жыл бұрын

Why are you doing so much WORK? 2^a = 3^b log(2^a) = log(3^b) a * log(2) = b * log(3) a/b = log(3)/log(2) (a + b)/b = a/b + b/b = a/b + 1 = 1 + log(3)/log(2) 8^((a + b)/b) = 8^(1 + log(3)/log(2)) = 216

@ReallyAmateurPianist Жыл бұрын

Nice video! I got the answer somewhat similar way, but with some differences ( e.g. using 2-based logarithm log2 ). Here's how I got there: 2^a = 3^b -> log2(2^a) = log2(3^b) -> a = b*log2(3) -> a/b = log2(3) 8^( (a+b) / b ) = 8^( (a/b) + 1 ) = 8 * 8^(a/b) = 8 * ( 2^(a/b) )^3 = 8 * ( 2^log2(3) )^3 = 8 * 3^3 = 216

@SyberMath Жыл бұрын

Nice work!