SOLUTION: I just can't seem to remember where to input my facts. my problem is log with base b 65 & log with base b (13/5) use the fact that log with base b5 is .8271 & log with b

Question 77926: I just can't seem to remember where to input my facts.
my problem is
log with base b 65 &
log with base b (13/5)
use the fact that log with base b5 is .8271 &
log with base b is 1.3181 to evaluate the expression.
How can I remember how to do this? Thanks in advance!!
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
logarithms are essentially exponents

so (when the base is the same) the log of the product (multiplying) of numbers is the sum of their logs, and the log of the quotient (dividing) of two numbers is the difference of their logs

5*13=65 so log(65)=log(5)+log(13) regardless of base...similarly log(13/5)=log(13)-log(5)

since logb(5)=.8271 and logb(13)=1.3181...logb(65)=2.1452 and logb(13/5)=0.491...(incidentally b=7)
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