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What is the value of
log sqrt10 ?
Answer:

What is the value of $\log \sqrt{10}$ ? $\newline$ Answer:

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Power property of logarithms

Full solution

Q. What is the value of

\log \sqrt{10}

?

\newline

Answer:

Identify Property: Identify the property used to expand $\log(\sqrt{10})$ . The power property of logarithms can be used to rewrite the square root in exponential form. Power property: $\log_b(m^{1/n}) = (\frac{1}{n}) \cdot \log_b(m)$
Express as Exponent: Express the square root of $10$ as an exponent. $\newline$ The square root of a number is the same as raising that number to the $1/2$ power. $\newline$ $\sqrt{10} = 10^{1/2}$
Apply Power Property: Apply the power property to $\log(\sqrt{10})$ . Using the power property from Step $1$ , we can write $\log(\sqrt{10})$ as: $\log(10^{1/2}) = (\frac{1}{2}) \cdot \log(10)$
Simplify Expression: Simplify the expression. $\newline$ Since $\log(10)$ is the common logarithm of $10$ , it is equal to $1$ . $\newline$ $(1/2) \times \log(10) = (1/2) \times 1 = 1/2$

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