SOLUTION: If log_8 3 = P and log_3 5 = Q, express log_{10} 5 in terms of P and Q. Your answer should no longer include any logarithms.

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Question 1177521: If log_8 3 = P and log_3 5 = Q, express log_{10} 5 in terms of P and Q. Your answer should no longer include any logarithms.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Given:
log%288%2C3%29=P
log%283%2C5%29=Q

Given those bases and arguments, it is almost certain that we will be working the problem using base 3 logarithms. So
log%283%2C8%29+=+1%2FP

Then



log%283%2C8%29+=+1%2FP
log%283%2C2%5E3%29+=+1%2FP
3%2Alog%283%2C2%29+=+1%2FP
log%283%2C2%29+=+1%2F%283P%29

And finally

log%2810%2C5%29+=+Q%2F%28Q%2B1%2F%283P%29%29

Simplify/change format if required....