# Math Help - Natural logarithms

1. ## Natural logarithms

Write this expression using only natural logarithms:

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

Thanks for any help!

2. 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 ...

$\log_b{a} = \frac{\ln{a}}{\ln{b}}$

3. 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 ??

4. review your log properties ...

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

$\ln\left(\frac{1}{5}\right) = \ln{1} - \ln{5} = 0 - \ln{5} = -\ln{5}$

5. so, ln(x-y) can't be reduced?

6. no ... you're stuck with it.

7. ok thanks for the help