SOLUTION: Solve the following equation for x log9(log5x)=1/2 (where the 9 is log base 9 and the 5 is log base 5)

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Question 1002148: Solve the following equation for x
log9(log5x)=1/2
(where the 9 is log base 9 and the 5 is log base 5)
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log%289%2C%28log%285%2Cx%29%29%29=1%2F2........change to the base 10 given log%285%2Cx%29

log%289%2C%28log%28x%29%2Flog%285%29%29%29=1%2F2.......change to the base 10 again

log%28%28log%28x%29%2Flog%285%29%29%29%2Flog%289%29=1%2F2

log%28%28log%28x%29%2Flog%285%29%29%29=%281%2F2%29log%289%29

log%28%28log%28x%29%2Flog%285%29%29%29=log%289%5E%281%2F2%29%29

log%28%28log%28x%29%2Flog%285%29%29%29=log%28sqrt%289%29%29

log%28%28log%28x%29%2Flog%285%29%29%29=log%283%29...if log same, we have

log%28x%29%2Flog%285%29=3

log%28x%29=3log%285%29

log%28x%29=log%285%5E3%29

log%28x%29=log%28125%29...if log same, we have

x=125





Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following equation for x
log9(log5x)=1/2
(where the 9 is log base 9 and the 5 is log base 5)
log+%289%2C+%28log+%285%2C+x%29%29%29+=+1%2F2

highlight%28highlight%28log+%285%2C+x%29+=+9%5E%281%2F2%29%29%29 --------- Changing to exponential form

log+%285%2C+x%29+=+3 ------- highlight%28highlight%289%5E%281%2F2%29%29%29 is equivalent to sqrt%289%29

x+=+5%5E3 ------- Changing to exponential form

highlight_green%28x+=+125%29