# Thread: Simplifying a log?

1. ## Simplifying a log?

Simplify the expression $2 ln e^3$

I came up with $e^{3}{2}$ It's e to the power of 3 to the power of 2.The answer is 6 and I don't see how you multiply 3 and 2 together.

Thanks

Jason

2. Properties that will help:
$\ln a^{b} = b \ln a$
$\ln e = 1$

3. Since the ln and e =1 then how do you take the 2 in front of the ln and multiply it by 3?Is it just 2(1)3=6?

4. You don't multiply ln and e. You're taking ln OF e. Just like you don't multiply sin and theta. You take the sin OF theta.

Now, read through the given hints again. Especially the FIRST property. You can take the exponent down in front of the logarithm.

5. I understand now. I figured the 2 went on top of the 3. I didn't think you could put the 3 in front of the 2 to make 3(2)lne.

6. Sure you can. This property of logarithms enables you to do that: $\ln a^{b} = b \ln a$ regardless if there is a constant in front or not.

7. If never seen a constant in front before, that's what messed me up. Thanks for the help.