Evaluate the logarithm. Round your answer to the nearest thousandth. log_(6)(42)~~

Problem Understanding: Understand the problem. We need to find the value of the logarithm of 42 with base 6, which is written as log₆(42). This means we are looking for the power to which we must raise 6 to get 42.Change of Base Formula: Use the change of base formula. The change of base formula allows us to write log₆(42) in terms of a logarithm with a more common base, such as 10 or e (natural logarithm). We will use base 10 for this calculation. The change of base formula is: log₆(42) = log₁₀(42) / log₁₀(6)Calculating Logarithms: Calculate the logarithms using a calculator. Using a calculator, we find: log₁₀(42) ≈ 1.6232 log₁₀(6) ≈ 0.7782Dividing Logarithms: Divide the two logarithms. Now we divide the values we obtained: log₆(42) ≈ 1.6232 / 0.7782 ≈ 2.0852Rounding the Result: Round the result to the nearest thousandth. Rounding 2.0852 to the nearest thousandth gives us: log₆(42) ≈ 2.085

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

log_(6)(42)~~

Evaluate the logarithm. $\newline$ Round your answer to the nearest thousandth. $\newline$ $\log _{6}(42) \approx$

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Algebra 1

Compare linear, exponential, and quadratic growth

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Q. Evaluate the logarithm.

\newline

Round your answer to the nearest thousandth.

\newline

\log _{6}(42) \approx

Problem Understanding: Understand the problem. $\newline$ We need to find the value of the logarithm of $42$ with base $6$ , which is written as $\log_6(42)$ . This means we are looking for the power to which we must raise $6$ to get $42$ .
Change of Base Formula: Use the change of base formula. $\newline$ The change of base formula allows us to write $\log_6(42)$ in terms of a logarithm with a more common base, such as $10$ or $e$ (natural logarithm). We will use base $10$ for this calculation. $\newline$ The change of base formula is: $\newline$ $\log_6(42) = \frac{\log_{10}(42)}{\log_{10}(6)}$
Calculating Logarithms: Calculate the logarithms using a calculator. $\newline$ Using a calculator, we find: $\newline$ $\log_{10}(42) \approx 1.6232$ $\newline$ $\log_{10}(6) \approx 0.7782$
Dividing Logarithms: Divide the two logarithms. $\newline$ Now we divide the values we obtained: $\newline$ $\log_6(42) \approx 1.6232 / 0.7782 \approx 2.0852$
Rounding the Result: Round the result to the nearest thousandth. $\newline$ Rounding $2.0852$ to the nearest thousandth gives us: $\newline$ $log_6(42) \approx 2.085$