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

2log_(6)(33)~~

Evaluate the logarithm. $\newline$ Round your answer to the nearest thousandth. $\newline$ $2 \log _{6}(33) \approx$

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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

2 \log _{6}(33) \approx

Problem Understanding: Understand the problem. $\newline$ We need to evaluate the expression $2\log_{6}(33)$ and round the result to the nearest thousandth.
Logarithm Power Rule: Apply the logarithm power rule. $\newline$ The power rule of logarithms states that $a\log_b(c) = \log_b(c^a)$ . We can apply this rule to simplify the expression: $\newline$ $2\log_6(33) = \log_6(33^2)$ .
Calculating $33$ Squared: Calculate $33$ squared. $\newline$ $33^2 = 33 \times 33 = 1089$ . $\newline$ Now the expression is $\log_{6}(1089)$ .
Evaluating the Logarithm: Evaluate the logarithm. $\newline$ We need to find the value of $\log_6(1089)$ . This can be done using a calculator or logarithm tables. $\newline$ Using a calculator, we find that $\log_6(1089) \approx 4.523$ .
Rounding the Result: Round the result to the nearest thousandth. $\newline$ Rounding $4.523$ to the nearest thousandth gives us $4.523$ , as there are no additional digits to consider.

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