SOLUTION: If log(base 3)2 = P And Log (base 3)13 = Q Express Log(base 78)52 in terms of P and Q

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Question 314103: If log(base 3)2 = P
And Log (base 3)13 = Q
Express Log(base 78)52 in terms of P and Q
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2C52%29
log%283%2C4%2A13%29
log%283%2C%282%5E2%2A13%29%29
By First Law of Logarithms,
log%283%2C+2%5E2%29+%2B+log%283%2C13%29
By Third Law of Logarithms,
2%2Alog+%283%2C2%29+%2B+log%283%2C13%29
2P%2BQ

Likewise,
log%283%2C+78%29
log%283%2C6%2A13%29
log%283%2C3%2A2%2A13%29
log%283%2C2%29%2Blog%283%2C3%29%2Blog%283%2C13%29
P%2B1%2BQ

Now, this is the unusual part. You want to convert this to log base 78.

Using the formula log%28b%2CM%29=%28ln+M%29%2F%28ln+b%29

log%2878%2C52%29+=%282P%2BQ%29%2F%28P%2BQ%2B1%29

For additional help with Logarithms for EASIER problems than this one, please see my own website. Click on my tutor name "rapaljer" anywhere in algebra.com. There you will see the link to my Homepage. Near the top of my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "College Algebra", and look for "Chapter 4" which is "Logarithms." I'm afraid I don't have much like this one however!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus