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How do i solve the equation 2^(3x-2)=3^(2x-1)

Guest Apr 1, 2017
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2^(3x-2)=3^(2x-1)      take the log of both sides

 

log 2^ (3x - 2)  =  log 3^(3x - 1)   and we can write

 

(3x - 2) log 2  =  (3x - 1) log 3  simplify

 

3x* log 2  - 2 log 2  =  3x log 3  - log 3   rearrange as

 

3log 2 * x - 3 log 3 * x   =  2log 2 - log 3       implify the left side

 

x [ 3 log 2  - 3 log 3 ]   = 2 log 2 - log 3       divide both sides by  [ 3 log 2  - 3 log 3 ]

 

x = [ 2 log 2 -  log 3 [ / [3 log 2 - 3 log 3 ]   ≈ -0.2365

 

 

 

cool cool cool

CPhill  Apr 1, 2017
edited by CPhill  Apr 1, 2017

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