How Do You Solve Logarithms with Square Roots?

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To solve logarithms involving square roots, one can rewrite the square root in exponential form, such as expressing the square root of e as e raised to the power of 1/2. Using the logarithmic identity, log_a(x^y) = y * log_a(x), allows simplification of the expression. For example, ln(√e) can be rewritten as ln(e^(1/2)), which simplifies to (1/2) * ln(e). This approach makes the logarithmic problem more manageable and easier to solve. Understanding these properties of logarithms is essential for tackling similar problems in calculus.
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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 loge[square root of e]
 
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Welcome to PF, Antisubs12.

Do you know another (equivalent) way to write

\log_{a}x^y = ?
 
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)
 
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.
 
ah thanks, i had forgotten there was a way to write square roots in exponential form. I can handle things from here. Thanks again.
 

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