# Logarithm exact value help

• Feb 2nd 2010, 01:54 PM
wallflower
Logarithm exact value help
The instructions say that, without a calculator, I have to find the exact value of each. I don't know how to do it at all, and no the last one is not a mistake. That;s what my book says exactly. I know it is odd.

ln √(e)

ln(e)^3

log√(2) 4
• Feb 2nd 2010, 02:02 PM
pickslides
Quote:

Originally Posted by wallflower
The instructions say that, without a calculator, I have to find the exact value of each. I don't know how to do it at all, and no the last one is not a mistake. That;s what my book says exactly. I know it is odd.

ln √(e)

ln(e)^3

log√(2) 4

$
\ln(\sqrt{e}) = \ln(e)^{\frac{1}{2}} = \frac{1}{2} \ln(e) = \frac{1}{2}\times 1 = \frac{1}{2}
$

Use this example to finish the rest.
• Feb 2nd 2010, 02:06 PM
wallflower
Thank you! I understand that! The only one I'm having trouble with are teh few that are like this one: log√(2) 4
• Feb 2nd 2010, 02:31 PM
e^(i*pi)
Quote:

Originally Posted by wallflower
Thank you! I understand that! The only one I'm having trouble with are teh few that are like this one: log√(2) 4

That's very ambiguous.

Do you mean

$log_{\sqrt2}(4)$ or $log(\sqrt{2^4})$.
• Feb 2nd 2010, 02:33 PM
wallflower
Oh. I'm sorry! I mean log (√2) 4 with two being the base and 4 being completely outside. Basically the first one you posted
• Feb 2nd 2010, 02:42 PM
e^(i*pi)
Quote:

Originally Posted by wallflower
Oh. I'm sorry! I mean log (√2) 4 with two being the base and 4 being completely outside. Basically the first one you posted

Okiedoke, for that one I'd use the change of base rule. I'm using log 2 as both numbers are powers of 2 but any base that is greater than 1 works

$log_{\sqrt2}(4) = \frac{log_2(4)}{log(\sqrt2)} = \frac{log_2(2^2)}{log_2(2^{1/2})} = \frac{2}{\frac{1}{2}} = 4$