# Natural logarithms

Printable View

• Dec 22nd 2008, 01:37 PM
live_laugh_luv27
Natural logarithms
Write this expression using only natural logarithms:

log (x-y) ----> (1/5 is the base)
1/5

Thanks for any help!
• Dec 22nd 2008, 01:53 PM
skeeter
Quote:

Originally Posted by live_laugh_luv27
Write this expression using only natural logarithms:

log (x-y) ----> (1/5 is the base)
1/5

Thanks for any help!

use the change of base formula ...

$\displaystyle \log_b{a} = \frac{\ln{a}}{\ln{b}}$
• Dec 22nd 2008, 01:56 PM
live_laugh_luv27
ok , and i got ln(x-y) / ln(1/5). Would I leave this as the answer, or would I distribute to get lnx - lny / ln1 - ln5 ??
• Dec 22nd 2008, 02:00 PM
skeeter
review your log properties ...

first off, $\displaystyle \ln(x-y) \neq \ln{x} - \ln{y}$ ,and

$\displaystyle \ln\left(\frac{1}{5}\right) = \ln{1} - \ln{5} = 0 - \ln{5} = -\ln{5}$
• Dec 22nd 2008, 02:10 PM
live_laugh_luv27
so, ln(x-y) can't be reduced?
• Dec 22nd 2008, 02:12 PM
skeeter
no ... you're stuck with it.
• Dec 22nd 2008, 02:15 PM
live_laugh_luv27
ok thanks for the help :)