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 Solve for x :

 

\(\log_{5} x + \log_{5} (x - 5) = 5\)

 

 A=

B=

There are two potential roots, A and B, where .\(A \leq B.\)

 Jun 6, 2018
 #1
avatar+101371 
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log 5 x + log 5 (x -5)  = 5

 

log 5 [ x * (x - 5) ]  = 5        we have that

 

5^5   =  x ( x - 5)

 

5^5  = x^2 - 5x      rearrange as

 

x^2  - 5x - 5^5  = 0     solving this we have that

 

x  = [5 + 5√501] / 2    or  x  =  [ 5 - 5√501] / 2

 

The second answer results in the log of a negative

 

So....the only answer  is     x  =  [  5 + 5√501] / 2

 

 

cool cool cool

 Jun 6, 2018

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