SOLUTION: If log base 8 of 3=r and log base 8 of 5=s, express log base 8 of 3/64 in terms of r and s.

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Question 154537: If log base 8 of 3=r and log base 8 of 5=s, express log base 8 of 3/64 in terms of r and s.
Answer by AnlytcPhil(1807) About Me  (Show Source):
You can put this solution on YOUR website!
If log base 8 of 3=r and log base 8 of 5=s, express log base 8 of 3/64 in terms of r and s.
If log%288%2C3%29=r and log%288%2C5%29=s, express log%288%2C%283%2F64%29%29 in terms of r and s.

log%288%2C%283%2F64%29%29

Use this logarithm rule:  log%28B%2C%28A%2FC%29%29=log%28B%2CA%29-log%28B%2CC%29

log%288%2C%283%2F64%29%29=log%288%2C3%29-log%288%2C64%29

Write 64 as 8%5E2

log%288%2C%283%2F64%29%29=log%288%2C3%29-log%288%2C8%5E2%29 

Use this logarithm rule on the last term: log%28B%2CA%5EC%29=C%2Alog%28B%2CA%29

log%288%2C%283%2F64%29%29=log%288%2C3%29-2%2Alog%288%2C8%29

Then use this logarithm rule on the last term: log%28B%2CB%29=1

log%288%2C%283%2F64%29%29=log%288%2C3%29-2%2A1

log%288%2C%283%2F64%29%29=r-2

s was not needed.

Edwin