What is the value of log_(3)((1)/(81)) ? Answer:

Recognize base and argument: Recognize the base and the argument of the logarithm. We are dealing with a logarithm with base 3 and the argument is 1/81. We need to express 1/81 as a power of 3 to simplify the logarithm.Express as power of 3: Express 1/81 as a power of 3. Since 81 is 3 raised to the power of 4 (3^4 = 81), 1/81 can be written as 3^-4.Apply logarithm definition: Apply the definition of logarithm. Using the fact that log base b of b^x is x, we can write log base 3 of 3^-4 as -4.Write final answer: Write down the final answer. The value of log base 3 of 1/81 is -4.

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What is the value of
log_(3)((1)/(81)) ?
Answer:

Evaluate. $\newline$ $\log _{3} \frac{1}{81}$ $\newline$ Write your answer in simplest form.

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Precalculus

Quotient property of logarithms

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Q. Evaluate.

\newline

\log _{3} \frac{1}{81}

\newline

Write your answer in simplest form.

Recognize base and argument: Recognize the base and the argument of the logarithm. We are dealing with a logarithm with base $3$ and the argument is $\frac{1}{81}$ . We need to express $\frac{1}{81}$ as a power of $3$ to simplify the logarithm.
Express as power of $3$ : Express $\frac{1}{81}$ as a power of $3$ . $\newline$ Since $81$ is $3$ raised to the power of $4$ ( $3^4 = 81$ ), $\frac{1}{81}$ can be written as $3^{-4}$ .
Apply logarithm definition: Apply the definition of logarithm. $\newline$ Using the fact that $\log_{b} b^{x} = x$ , we can write $\log_{3} 3^{-4}$ as $-4$ .
Write final answer: Write down the final answer. $\newline$ The value of $\log_{3} \frac{1}{81}$ is $-4$ .