SOLUTION: Log5 1/625. the question asks evaluate the logarithm.

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Question 41720: Log5 1/625. the question asks evaluate the logarithm.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
log%285%2C+1%2F625%29+=+x
rewrite this as
1%2F625+=+5%5Ex
multiply both sides by 625
1+=+5%5Ex+%2A+625
625+=+5%5E4
1+=+5%5Ex%2A5%5E4
1+=+5%5E%28x+%2B+4%29
anything to the zero power is 1
If x = -4, then
1+=+5%5E%28-4+%2B4%29
This is an identity
check
1%2F625+=+5%5Ex
1%2F625+=+5%5E%28-4%29
1%2F%285%5E4%29+=+5%5E%28-4%29
5%5E%28-4%29+=+5%5E%28-4%29
OK