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What is the value of
log_(8)((1)/(8)) ?
Answer:

Evaluate. $\newline$ $\log _{8} \frac{1}{8}$ $\newline$ Write your answer in simplest form.

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Full solution

Q. Evaluate.

\newline

\log _{8} \frac{1}{8}

\newline

Write your answer in simplest form.

Define Logarithm Function: We need to find the value of the logarithm of $\frac{1}{8}$ to the base $8$ . The logarithm function $\log_b(a)$ answers the question ＂to what power must $b$ be raised, to get $a$ ?＂. In this case, we are looking for the power to which $8$ must be raised to get $\frac{1}{8}$ .
Convert $1/8$ to $8^{-1}$ : We know that $1/8$ is the same as $8$ raised to the power of $-1$ , because $8^{-1} = 1/8$ .
Apply Logarithm Property: Therefore, $\log_{8} \frac{1}{8}$ is the same as $\log_{8} 8^{-1}$ . According to the properties of logarithms, $\log_{b}(b^{x}) = x$ . So, $\log_{8} 8^{-1}$ is $-1$ .
Find Log base $8$ of $1/8$ : We have found the value of the logarithm without needing to perform any complex calculations. The value of log base $8$ of $1/8$ is $-1$ .

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