SOLUTION: log5 sqrt(x)= log(sqrt(x)) 5

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Question 1197096: log5 sqrt(x)= log(sqrt(x)) 5
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log%285%2C+%28sqrt%28x%29%29%29=+log%28sqrt%28x%29%2C+%285%29%29.........change to base 10
log%28sqrt%28x%29%29%2Flog%28%285%29%29=+log%28+%285%29%29%2F+log%28sqrt%28x%29%29.....cross multiply
log%28sqrt%28x%29%29%2A+log%28sqrt%28x%29%29=+log%28+%285%29%29%2Alog%28%285%29%29
log%5E2%28sqrt%28x%29%29=+log%5E2%28+%285%29%29....if log same, then
sqrt%28x%29=++5
x=++25

Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.


            This problem has  TWO  solutions,  not one.
            In the post by @MathLover1 second possible solution is  LOST.
            So I came to bring a full correct solution. 


log%285%2C+%28sqrt%28x%29%29%29 = log%28sqrt%28x%29%2C+%285%29%29.........change to base 10 

log%28sqrt%28x%29%29%2Flog%28%285%29%29 = log%28%285%29%29%2F+log%28sqrt%28x%29%29........cross multiply

log%28%28sqrt%28x%29%29%29%2A+log%28%28sqrt%28x%29%29%29 = log%28%285%29%29%2Alog%28%285%29%29

%28log%28%28sqrt%28x%29%29%29%29%5E2 = %28log%28%285%29%29%29%5E2........it implies

log%28%28sqrt%28%28x%29%29%29%29 =  +/- log%28%285%29%29


If log%28%28sqrt%28x%29%29%29 =  log%28%285%29%29   then  sqrt(x) =  5;  hence,  x = 25.

If log%28%28sqrt%28x%29%29%29 =  -log%28%285%29%29  then  sqrt(x) =  1/5;  hence,  x = 1/25.


ANSWER.  There are two solutions,  x= 25  and/or  x = 1/25.

Solved (in a right way).