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avatar+271 

What is the exact solution to the equation

 

 

Please and thank you! 0^>

 Dec 13, 2018
 #1
avatar+98034 
+2

Yep....a little tough!!!.....the idea is to isolate x

 

2^(2x)   = 5^(x - 1)         take the log of both sides

 

log 2^(2x)   =  log 5^(x - 1)       using a log property, we have

 

2x* log 2  = (x - 1) log 5       simplify

 

(2log 2) * x   =  xlog 5  - log 5          rearrange as

 

log 5  =   x log 5 - (2log2) x          factor out x on the right

 

log 5  =  x [ log 5 - 2log2 ]         divide  both sides by  [ log 5 - 2log 2]

 

 

log 5

___________   =   x           {second answer }

log 5 - 2 log 2

 

 

Note Phoenix that I used log  instead of Ln.....just substitute.....the answers will be the same, numerically !!!!!!

 

 

 

cool cool cool

 Dec 13, 2018
 #2
avatar+271 
+1

Thank you very much for explaining this difficult one for me. Substitution is much easier to work with.

PhoenixForever  Dec 13, 2018

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