Evaluate the logarithm. Round your answer to the nearest thousandth. log_(2)(75)~~

Problem Understanding: Understand the problem. We need to find the value of the logarithm of 75 with base 2, which is written as log₂(75). This means we are looking for the power to which 2 must be raised to get 75.Calculating Logarithm Value: Use a calculator or logarithm properties to find the value. Since 75 is not a power of 2, we will need to use a calculator or logarithm properties to approximate the value of log₂(75). Using a calculator, we input log₂(75) or use the change of base formula: log₂(75) = log(75) / log(2).Using Change of Base Formula: Calculate the value using the change of base formula. Using a scientific calculator, we find: log(75) ≈ 4.317488 log(2) ≈ 0.693147 Now, divide log(75) by log(2) to get log₂(75): log₂(75) ≈ 4.317488 / 0.693147 ≈ 6.228819Rounding the Result: Round the result to the nearest thousandth. Rounding 6.228819 to the nearest thousandth gives us 6.229.

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

log_(2)(75)~~

Evaluate the logarithm. $\newline$ Round your answer to the nearest thousandth. $\newline$ $\log _{2}(75) \approx$

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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 _{2}(75) \approx

Problem Understanding: Understand the problem. $\newline$ We need to find the value of the logarithm of $75$ with base $2$ , which is written as $\log_2(75)$ . This means we are looking for the power to which $2$ must be raised to get $75$ .
Calculating Logarithm Value: Use a calculator or logarithm properties to find the value. $\newline$ Since $75$ is not a power of $2$ , we will need to use a calculator or logarithm properties to approximate the value of $\log_{2}(75)$ . $\newline$ Using a calculator, we input $\log_{2}(75)$ or use the change of base formula: $\log_{2}(75) = \frac{\log(75)}{\log(2)}$ .
Using Change of Base Formula: Calculate the value using the change of base formula. $\newline$ Using a scientific calculator, we find: $\newline$ $\log(75) \approx 4.317488$ $\newline$ $\log(2) \approx 0.693147$ $\newline$ Now, divide $\log(75)$ by $\log(2)$ to get $\log_2(75)$ : $\newline$ $\log_2(75) \approx \frac{4.317488}{0.693147} \approx 6.228819$
Rounding the Result: Round the result to the nearest thousandth. $\newline$ Rounding $6.228819$ to the nearest thousandth gives us $6.229$ .