Evaluate the logarithm. Round your answer to the nearest thousandth. 3log_(9)((1)/(12))~~◻

Understand the problem: Understand the problem. We need to evaluate the logarithm of (1/12) with base 9, then multiply the result by 3.Convert to common base: Convert the base of the logarithm to a common base, such as base 10 or base e (natural logarithm). Using the change of base formula: log_b(a) = log_c(a) / log_c(b), where c is the new base. Let's use base 10 for this problem. log_9(1/12) = log(1/12) / log(9)Calculate log values: Calculate the value of log(1/12) and log(9) using a calculator. log(1/12) ≈ -1.079 log(9) ≈ 0.954Divide to find log: Divide the two values to find the value of log_9(1/12). log_9(1/12) ≈ -1.079 / 0.954 ≈ -1.131Multiply by 3: Multiply the result by 3 to find the value of 3log_9(1/12). 3log_9(1/12) ≈ 3 * (-1.131) ≈ -3.393Round the result: Round the result to the nearest thousandth. 3log_9(1/12) ≈ -3.393 (rounded to the nearest thousandth)

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Evaluate the logarithm.
Round your answer to the nearest thousandth.

3log_(9)((1)/(12))~~◻

Evaluate the logarithm. $\newline$ Round your answer to the nearest thousandth. $\newline$ $3 \log _{9}\left(\frac{1}{12}\right) \approx \square$

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Algebra 1

Compare linear, exponential, and quadratic growth

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Q. Evaluate the logarithm.

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Round your answer to the nearest thousandth.

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3 \log _{9}\left(\frac{1}{12}\right) \approx \square

Understand the problem: Understand the problem. $\newline$ We need to evaluate the logarithm of $\frac{1}{12}$ with base $9$ , then multiply the result by $3$ .
Convert to common base: Convert the base of the logarithm to a common base, such as base $10$ or base $e$ (natural logarithm). $\newline$ Using the change of base formula: $\log_b(a) = \frac{\log_c(a)}{\log_c(b)}$ , where $c$ is the new base. $\newline$ Let's use base $10$ for this problem. $\newline$ $\log_9(\frac{1}{12}) = \frac{\log(\frac{1}{12})}{\log(9)}$
Calculate log values: Calculate the value of $\log(\frac{1}{12})$ and $\log(9)$ using a calculator. $\newline$ $\log(\frac{1}{12}) \approx -1.079$ $\newline$ $\log(9) \approx 0.954$
Divide to find log: Divide the two values to find the value of $\log_9(\frac{1}{12})$ . $\log_9(\frac{1}{12}) \approx \frac{-1.079}{0.954} \approx -1.131$
Multiply by $3$ : Multiply the result by $3$ to find the value of $3\log_9(\frac{1}{12})$ . $3\log_9(\frac{1}{12}) \approx 3 \times (-1.131) \approx -3.393$
Round the result: Round the result to the nearest thousandth. $\newline$ $3\log_9(\frac{1}{12}) \approx -3.393$ (rounded to the nearest thousandth)