What is the value of log ((1)/(100))? Answer:

Identify Base: Question prompt: What is the value of log((1)/(100))?Apply Definition: Recognize the base of the logarithm. The logarithm given does not specify a base, which means it is a common logarithm and has a base of 10.Express as Power: Apply the definition of a common logarithm. The common logarithm log base 10 of a number is the power to which the base (10) must be raised to obtain that number.Rewrite Logarithm: Express 100 as a power of 10. 100 is equal to 10^2.Apply Power Rule: Rewrite the logarithm using the power of 10. log((1)/(100)) can be rewritten as log(10^(-2)) because 1/100 is the same as 10 to the power of -2.Evaluate Logarithm: Apply the power rule of logarithms. The power rule of logarithms states that log(a^b) = b * log(a). Therefore, log(10^(-2)) = -2 * log(10).Multiply Exponent: Evaluate log(10). Since the base of the logarithm is 10, log(10) is equal to 1.Multiply the exponent by the value of log(10). -2 * log(10) is equal to -2 * 1, which simplifies to -2.

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What is the value of
log ((1)/(100))?
Answer:

Evaluate. $\newline$ $\log \frac{1}{100}$ $\newline$ Write your answer in simplest form.

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Precalculus

Quotient property of logarithms

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Q. Evaluate.

\newline

\log \frac{1}{100}

\newline

Write your answer in simplest form.

Identify Base: Question prompt: What is the value of $\log\left(\frac{1}{100}\right)$ ?
Apply Definition: Recognize the base of the logarithm. $\newline$ The logarithm given does not specify a base, which means it is a common logarithm and has a base of $10$ .
Express as Power: Apply the definition of a common logarithm. $\newline$ The common logarithm $\log_{10}$ of a number is the power to which the base $10$ must be raised to obtain that number.
Rewrite Logarithm: Express $100$ as a power of $10$ . $100$ is equal to $10^2$ .
Apply Power Rule: Rewrite the logarithm using the power of $10$ . $\log\left(\frac{1}{100}\right)$ can be rewritten as $\log(10^{-2})$ because $\frac{1}{100}$ is the same as $10$ to the power of $-2$ .
Evaluate Logarithm: Apply the power rule of logarithms. $\newline$ The power rule of logarithms states that $\log(a^b) = b \cdot \log(a)$ . Therefore, $\log(10^{-2}) = -2 \cdot \log(10)$ .
Multiply Exponent: Evaluate $\log(10)$ . Since the base of the logarithm is $10$ , $\log(10)$ is equal to $1$ .
Multiply Exponent: Evaluate $\log(10)$ . Since the base of the logarithm is $10$ , $\log(10)$ is equal to $1$ .Multiply the exponent by the value of $\log(10)$ . $-2 \times \log(10)$ is equal to $-2 \times 1$ , which simplifies to $-2$ .