What is the value of log sqrt10 ? 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)) = (1/n) * log_b(m)Express as Exponent: Express the square root of 10 as an exponent. The square root of a number is the same as raising that number to the 1/2 power. 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)) = (1/2) * log(10)Simplify Expression: Simplify the expression. Since log(10) is the common logarithm of 10, it is equal to 1. (1/2) * log(10) = (1/2) * 1 = 1/2

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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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Precalculus

Power property of logarithms

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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 $1$ . $\newline$ $(1/2) \times \log(10) = (1/2) \times 1 = 1/2$