SOLUTION: how to solve this equation: (log x)^2=2log x (the base is 5)

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Question 595104: how to solve this equation:
(log x)^2=2log x (the base is 5)

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
%28log%285%2C+x%29%29%5E2=2%2Alog%285%2C+x%29 (the base is 5)
Itīs easier to see it if we change variables for a while, making
y=log%285%2C+x%29
Then, we can write it as
y%5E2=2y and then as
y%5E2-2y=0 and as
%28y-2%29y=0
The solutions are y=2 and y=0 .
y=2 means log%285%2C+x%29=2 so x=5%5E2=25
y=0 means log%285%2C+x%29=0 so x=5%5E0=1