# Natural log problem

• Mar 1st 2009, 04:25 PM
galanm
Natural log problem
I've solved this problem a couple different ways and come up with different answers and I have had a couple other people come up with different answers. What log basic am I missing?

Given that ln a = 5 and ln b = 7 evaluate the following:

ln a2 be2
• Mar 1st 2009, 04:48 PM
arpitagarwal82
Is it
$\ln a^2 \ln be^2$

or

$\ln a^2 \ln (be)^2$

Assuming its $\ln a^2 \ln be^2$

= 2\ln a ( \ln b + 2\ln e)
= 2\ln a ( \ln b +2)
2 x 5 ( 7 + 2)
2 x 5 x 9
90
• Mar 1st 2009, 04:51 PM
galanm
Problem is presented as:

ln a^2be^2 no spaces between variables
• Mar 1st 2009, 05:04 PM
arpitagarwal82
then its
$\n a^2be^2$

$= \ln a^2 + \ln b + \ln e^2$

$= 2\ln a + \ln b + 2\ln e$

= 2 x 5 + 7 + 2 x 1
= 19