SOLUTION: Let P = \log_8 3 and Q = \log_3 5. Express \log_{15} 72 in terms of P and Q. Your answer should no longer include any logarithms.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Let P = \log_8 3 and Q = \log_3 5. Express \log_{15} 72 in terms of P and Q. Your answer should no longer include any logarithms.       Log On


   

Question 1209839: Let P = \log_8 3 and Q = \log_3 5. Express \log_{15} 72 in terms of P and Q. Your answer should no longer include any logarithms.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Given:

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

To find:

log%2815%2C72%29

log%2815%2C72%29=log%28b%2C72%29%2Flog%28b%2C15%29
log%28b%2C72%29=log%28b%2C8%29%2Blog%28b%2C9%29

log%28b%2C15%29=log%28b%2C3%29%2Blog%28b%2C5%29


With the given information, we want to use base 3 logarithms.

log%288%2C3%29=P --> log%283%2C8%29=1%2FP



The result can be written in many different forms....

ANSWER: %28%281%2FP%29%2B2%29%2F%281%2BQ%29