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

5log_(2)(48)~~

Evaluate the logarithm. $\newline$ Round your answer to the nearest thousandth. $\newline$ $5 \log _{2}(48) \approx$

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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

5 \log _{2}(48) \approx

Problem Understanding: Understand the problem. $\newline$ We need to evaluate the expression $5\log_2(48)$ 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: $\newline$ $5\log_2(48) = \log_2(48^5)$ .
Calculating $48^5$ : Calculate $48^5$ . $\newline$ Using a calculator, we find that $48^5 = 48 \times 48 \times 48 \times 48 \times 48 = 254803968$ .
Evaluating $\log_2(254803968)$ : Evaluate $\log_2(254803968)$ . $\newline$ Using a calculator with a base $-2$ logarithm function, we find that $\log_2(254803968) \approx 27.9307$ .
Rounding to Nearest Thousandth: Round the result to the nearest thousandth. $\newline$ Rounding $27.9307$ to the nearest thousandth gives us $27.931$ .

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