# Can't figure out what I'm doing wrong in this logarithm contraction...

• Feb 17th 2010, 01:15 AM
andrewtheart
Can't figure out what I'm doing wrong in this logarithm contraction...
Hey guys --

I compacted an expression using the base change, power, quotient, and product rules of logarithms -- however, my compacted expression is not evaluating to the same result as the original equation.

I've looked over this a few times and for the life of me cannot see my mistake -- maybe one of you can?

Thanks --

Andrew

http://imgur.com/tbyWP.jpg

http://imgur.com/OBX5Q.jpg
• Feb 17th 2010, 02:59 AM
HallsofIvy
You have
$\frac{log_2(T^4)}{log_2(8)}$
and then
$log_2(T^4)- log_2(8)$

That is incorrect: the rule is log(a/b)= log(a)- log(b), not log(a)/log(b).

Instead use the fact that $log_2(8)= log_2(2^3)= 3$.

$\frac{log_2(T^4)}{log_2(8)}= \frac{1}{3}log_2(T^4)= log_2(T^{4/3})$
• Feb 17th 2010, 03:47 AM
andrewtheart
Ah, what a silly mistake. Thanks for catching that.

(Doing my work at 3 in the morning is a mistake in general)

Thanks for the help -- I greatly appreciate it. I can already see you make the Math Help Forum a great resource for everyone. Good for you!