SOLUTION: {{{5^(x-1)= 5^x-5}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: {{{5^(x-1)= 5^x-5}}}      Log On


   

Question 748288: 5%5E%28x-1%29=+5%5Ex-5
Found 2 solutions by Alan3354, tommyt3rd:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
5%5E%28x-1%29=+5%5Ex-5
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Sub u for 5^(x-1)
u = 5u - 5
u = 5/4
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5^(x-1) = 5/4
5^x = 25/4
x*log(5) = log(25/4)
x = log(6.25)/log(5)
x =~ 1.13864688

Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
we will denote log base 5 as log5
5%5E%28x-1%29=+5%5Ex-5

5%5E%28x-1%29-5%5E%28x-1%29%2B5=+5%5Ex-5%5E%28x-1%29-5%2B5

5%5Ex-%285%5Ex%29%2F5=+5

5%5Ex%2A%281-1%2F5%29=5

5%5Ex=5%2F%284%2F5%29

5%5Ex=25%2F4

%0D%0Alog5%285%5Ex%29=log5%2825%2F4%29%0D%0A

%0D%0Ax=log5%2825%29-log5%284%29=2-log5%284%29%0D%0A



:)