SOLUTION: Find the logarithm using the change-of-base formula. Round to the nearest ten-thousandth. log8.1 5.6

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Find the logarithm using the change-of-base formula. Round to the nearest ten-thousandth. log8.1 5.6      Log On


   

Question 285750: Find the logarithm using the change-of-base formula. Round to the nearest ten-thousandth.
log8.1 5.6
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The change of base formula is:
log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29
We will use this to change the base from 8.1 to a expression of logarithms of a base your calculator "knows", base 10 or base e (ln).

To base 10:
log%288.1%2C+%285.6%29%29+=+log%28%285.6%29%29%2Flog%28%288.1%29%29
To base e:
log%288.1%2C+%285.6%29%29+=+ln%285.6%29%2Fln%288.1%29

Either of these work and they will both give you the same answer. I'll leave it up to you to choose one and use your calculator on it. (Just be sure to find the two logarithms first and then divide.)