## evaluating natural log expressions: ln sq rt e w/o calc

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### evaluating natural log expressions: ln sq rt e w/o calc

I need to evaluate the following without a calculator:

ln sq.rt.e (sorry I can't find notation for square root). Does this mean the natural log of e to the 1/2 power?
santaclaus

Posts: 41
Joined: Tue Mar 03, 2009 12:17 am

### Re: evaluating natural logs

santaclaus wrote:I need to evaluate the following without a calculator:

ln sq.rt.e (sorry I can't find notation for square root). Does this mean the natural log of e to the 1/2 power?

if the question is evaluate ...

$\ln\left(\sqrt{e}\right)$

then

$\ln\left(\sqrt{e}\right)=\ln\left((e)^{1/2}\right)=\frac{1}{2}\ln(e)=\frac{1}{2}\cdot 1=\frac{1}{2}$

Martingale

Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA

santaclaus wrote:ln sq.rt.e

Does this mean the natural log of e to the 1/2 power?

Yes, a square root is the same as a one-half power. For clarification, try here.

stapel_eliz

Posts: 1720
Joined: Mon Dec 08, 2008 4:22 pm

### Re: evaluating natural log expressions: ln sq rt e w/o calc

ok, so how about ln (1/sq.rt.e)?

would it be -1/2?
santaclaus

Posts: 41
Joined: Tue Mar 03, 2009 12:17 am

Yup!

stapel_eliz

Posts: 1720
Joined: Mon Dec 08, 2008 4:22 pm