How to solve this exponential equation? 2^(2x)3^x=4^(3x+1)

Kailyn Hamilton

Kailyn Hamilton

Answered question

2022-11-17

How to solve this exponential equation? 2 2 x 3 x = 4 3 x + 1
I haven't been able to find the correct answer to this exponential equation:
2 2 x 3 x = 4 3 x + 1 2 2 x 3 x = 2 2 × 2 x × 3 x 4 3 x + 1 = 4 3 × 4 x × 4 6 x × 4 = 4 x × 256 x log 6 6 + log 6 4 = x log 6 4 + log 6 256 x + log 6 4 = x log 6 4 + log 6 256 x x log 6 4 = log 6 256 log 6 4 x ( 1 log 6 4 ) = log 6 256 log 6 4 x = log 6 256 log 6 4 1 log 6 4 x = 10.257
so when I checked the answer I wasn't able to make them equal, I have tried variants of this method but I feel I'm missing something..

Answer & Explanation

Zoe Andersen

Zoe Andersen

Beginner2022-11-18Added 16 answers

I think the problem with your solution might be here:
2 2 x 3 x => 2 2 2 x 3 x
4 3 x + 1 => 4 3 4 x 4
since a b c = ( a b ) c and not a b a c . So for instance:
4 3 x + 1 => 4 x 4 x 4 x 4

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