# Thread: Natural Logarithms Help Plz!

1. ## Natural Logarithms Help Plz!

I managed to do all of my homework except this one:

How do you solve the equation: ln x - ln 5= -1??

2. $\begin{gathered}
\ln x - \ln 5 = - 1 \hfill \\
\ln \frac{x}
{5} = - 1 \hfill \\
\Leftrightarrow \frac{x}
{5} = e^{ - 1} \hfill \\
\Leftrightarrow x = 5e^{ - 1} \hfill \\
\end{gathered}
$

3. how did you do that? You divide the numbers x and 5 together?

And after that I just find out what e^-1 is?

4. Originally Posted by topaz192
how did you do that? You divide the numbers x and 5 together?
it is a rule

$\log_a x - \log_a y = \log_a \frac xy$

And after that I just find out what e^-1 is?
no. leave it as e^{-1}. or you can write the answer as 5/e if you wish

5. ok i thought e cant get left in the answer?

6. Originally Posted by topaz192
ok i thought e cant get left in the answer?

7. yea it did. so how do you get an answer? isnt e^-1?

8. Originally Posted by topaz192
yea it did. so how do you get an answer? isnt e^-1?
um, just plug it into your calculator

9. ok! thanks for your time! = )

10. Originally Posted by topaz192
ok! thanks for your time! = )
you're welcome