SOLUTION: Solve for x: {{{log(x,7)*log(7,5)=2}}}

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Question 1118205: Solve for x: log%28x%2C7%29%2Alog%287%2C5%29=2
Found 2 solutions by stanbon, greenestamps:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x: log(x,7)*log(7,5)=2
log(7)/log(x) *log(5)/log(7) = 2
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log(5)*log(x) = 2
log(x) = 2/log(5)
log(x) = 2.8614
x = 726.7
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Cheers,
Stan H.
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Use the change-of-base formula:



Then the last equation in that string says

x%5E2+=+5
x+=+sqrt%285%29

Note that people who are familiar with logarithms simply look at the original equation

log%28x%2C7%29%2Alog%287%2C5%29=2

and "cancel" the 7's to get log%28x%2C5%29+=+2, then proceed from there.