How Do You Solve Logarithms with Square Roots?

[Antisubs12]

I've been working on logarithms in my calculus class and I came acrossed one with a square root. Since I am new to these types of problems I'm not sure how to work with this yet.

How would I solve something such as log_e[square root of e]

 

[neutrino]

Welcome to PF, Antisubs12.

Do you know another (equivalent) way to write

$$\log_{a}x^y = ?$$

 

[cristo]

Well, $\ln\sqrt{e}=\ln e^{1/2}=\frac{1}{2}\ln{e}=\frac{1}{2}$. Where the second equality comes from the rule ln(a)^b=b ln(a)

 

[JonF]

how would you write square root of e in expediential form? After you do that ask your self what law of logs will help you make the problem more workable.

 

[Antisubs12]

ah thanks, i had forgotten there was a way to write square roots in exponential form. I can handle things from here. Thanks again.