Struggling to finish an exponential equation I have this exponential equation I tried solving but I'm stuck at the end. The problem is this: 4^x-3^(x-1/2)=3^(x+1/2)-2^(2x-1)

blogswput 2022-09-11 Answered
Struggling to finish an exponential equation
I have this exponential equation I tried solving but I'm stuck at the end.
The problem is this:
4 x 3 x 1 2 = 3 x + 1 2 2 2 x 1
And my approach is this:
2 2 x + 2 2 x 1 = 3 x + 1 2 + 3 x 1 2
2 2 x ( 1 + 2 1 ) = 3 x ( 3 1 2 + 3 1 2 )
2 2 x 3 2 = 3 x ( 3 + 1 3 )
2 2 x 3 2 = 3 x ( 3 2 + 1 3 )
2 2 x 3 2 = 3 x 4 3 3 --> here I have rationalized the fraction
2 2 x 3 x = 4 3 3 2 3
( 2 2 3 ) x = 8 3 9
Now I hope I didn't make an error. How should I proceed from this point? Is there another way around this problem?
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Answers (1)

Maleah Lester
Answered 2022-09-12 Author has 12 answers
I think you did not make a mistake.
Your last equation it's
( 2 3 ) 2 x = ( 2 3 ) 3
because
8 3 9 = 8 3 8 1 = 8 27 = 2 3 3 3 = 2 3 ( 3 ) 3 = ( 2 3 ) 3 .

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