Evaluate the logarithm. Round your answer to the nearest thousandth. log_(5)(200)~~

Understand Problem: Understand the problem and identify the base of the logarithm. We need to evaluate the logarithm of 200 with base 5. This means we are looking for the power to which 5 must be raised to get 200.Change of Base: Use the change of base formula to convert the base 5 logarithm to a common logarithm. The change of base formula states that log base b of a can be written as (log a) / (log b). We will use the natural logarithm (ln) for this purpose. log_(5)(200) = ln(200) / ln(5)Calculate Logarithms: Calculate the natural logarithm of 200 and 5 using a calculator. ln(200) ≈ 5.2983 ln(5) ≈ 1.6094Divide Logarithms: Divide the natural logarithm of 200 by the natural logarithm of 5. (5.2983) / (1.6094) ≈ 3.2925Round Result: Round the result to the nearest thousandth. 3.2925 rounded to the nearest thousandth is 3.293.

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

log_(5)(200)~~

Evaluate the logarithm. $\newline$ Round your answer to the nearest thousandth. $\newline$ $\log _{5}(200) \approx$

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Math Problems

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 _{5}(200) \approx

Understand Problem: Understand the problem and identify the base of the logarithm. $\newline$ We need to evaluate the logarithm of $200$ with base $5$ . This means we are looking for the power to which $5$ must be raised to get $200$ .
Change of Base: Use the change of base formula to convert the base $5$ logarithm to a common logarithm. $\newline$ The change of base formula states that $\log_{b}a$ can be written as $(\log a) / (\log b)$ . We will use the natural logarithm $(\ln)$ for this purpose. $\newline$ $\log_{5}(200) = \frac{\ln(200)}{\ln(5)}$
Calculate Logarithms: Calculate the natural logarithm of $200$ and $5$ using a calculator. $\newline$ $\ln(200) \approx 5.2983$ $\newline$ $\ln(5) \approx 1.6094$
Divide Logarithms: Divide the natural logarithm of $200$ by the natural logarithm of $5$ . $\newline$ $\left(\frac{5.2983}{1.6094}\right) \approx 3.2925$
Round Result: Round the result to the nearest thousandth. $3.2925$ rounded to the nearest thousandth is $3.293$ .