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$Express the given expression as an integer or as a fraction in simplest form. log(10^(2)) Answer:$

Express the given expression as an integer or as a fraction in simplest form. $\newline$ $\log \left(10^{2}\right)$ $\newline$ Answer:

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Evaluate logarithms

Full solution

Q. Express the given expression as an integer or as a fraction in simplest form.

\newline

\log \left(10^{2}\right)

\newline

Answer:

Identify base and argument: Identify the base of the logarithm and the argument. $\newline$ The base of the logarithm is $10$ , which is the common logarithm base, and the argument is $10^{2}$ .
Apply logarithm power rule: Apply the logarithm power rule. $\newline$ The power rule of logarithms states that $\log_b(a^n) = n \cdot \log_b(a)$ , where $b$ is the base, $a$ is the argument, and $n$ is the exponent. $\newline$ For our expression, $\log(10^{2})$ can be rewritten as $2 \cdot \log(10)$ .
Evaluate $\log(10)$ : Evaluate $\log(10)$ . $\newline$ Since the base of the logarithm is $10$ and the argument is also $10$ , $\log(10)$ is equal to $1$ because $10^1 = 10$ .
Multiply exponent by log( $10$ ): Multiply the exponent by the value of $\log(10)$ . Now we have $2 \times \log(10)$ which is $2 \times 1$ . This simplifies to $2$ .

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