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

6log_(7)(681)~~

Evaluate the logarithm. $\newline$ Round your answer to the nearest thousandth. $\newline$ $6 \log _{7}(681) \approx$

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Compare linear, exponential, and quadratic growth

Full solution

Q. Evaluate the logarithm.

\newline

Round your answer to the nearest thousandth.

\newline

6 \log _{7}(681) \approx

Problem Understanding: Understand the problem. $\newline$ We need to evaluate the expression $6\log_{7}(681)$ and round the result to the nearest thousandth.
Simplifying the Expression: Use the properties of logarithms to simplify the expression. $\newline$ The expression $6\log_{7}(681)$ can be rewritten as $\log_{7}(681^6)$ because of the power rule of logarithms, which states that $a\log_{b}(c) = \log_{b}(c^a)$ .
Calculating the Value: Calculate the value of $681^6$ . $\newline$ This step involves a large number calculation which is typically done using a calculator.
Evaluating the Logarithm: Evaluate the logarithm $\log_{7}(681^6)$ . Since the calculation of $681^6$ is impractical without a calculator, we will use a calculator to directly evaluate $6\log_{7}(681)$ .
Rounding the Result: Round the result to the nearest thousandth. $\newline$ After using a calculator, we find that $6\log_{7}(681)$ is approximately $18.404$ . Rounding this to the nearest thousandth gives us $18.404$ .

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