SOLUTION: log5(log5 x)=1

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Question 238165: log5(log5 x)=1
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
When the variable you're solving for is in the argument of a logarithm, the most common way to solve the problem is to rewrite the logarithmic equation in exponential form. With this problem's log of a log we will have to do thsi twice.

Remember that log%28a%2C+%28b%29%29+=+x is equivalent to b+=+a%5Ex. We will use this twice in succession on your equation:
log%285%2C+%28log%285%2C+%28x%29%29%29%29+=+1
which in exponential form is:
log%285%2C+%28x%29%29+=+5%5E1
which simplifies to
log%285%2C+%28x%29%29+=+5
Rewriting this in exponential form we get:
x+=+5%5E5
which simplifies to
x+=+3125