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

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
santaclaus
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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?

Martingale
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### Re: evaluating natural logs

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

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

stapel_eliz
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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.

santaclaus
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Joined: Tue Mar 03, 2009 12:17 am
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### 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?

stapel_eliz
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Yup!