Evaluate the logarithm. Round your answer to the nearest thousandth. log_(7)(25)~~

Understand the Problem: Understand the problem. We need to find the value of the logarithm of 25 with base 7, which is written as log₇(25). This means we are looking for the power to which we must raise 7 to get 25.Use Calculator or Properties: Use a calculator or logarithm properties to find the value. Since 25 is not a power of 7, we will need to use a calculator or logarithm properties to approximate the value of log₇(25). If a calculator with the ability to compute logarithms with any base is not available, we can use the change of base formula: log₇(25) = log(25) / log(7)Calculate Using Formula: Calculate using the change of base formula. Using a scientific calculator, we find: log(25) ≈ 1.39794 log(7) ≈ 0.84510 Now, divide the two values to get log₇(25): log₇(25) ≈ 1.39794 / 0.84510 ≈ 1.654Round the Answer: Round the answer to the nearest thousandth. Rounding 1.654 to the nearest thousandth gives us 1.654.

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

log_(7)(25)~~

Evaluate the logarithm. $\newline$ Round your answer to the nearest thousandth. $\newline$ $\log _{7}(25) \approx$

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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 _{7}(25) \approx

Understand the Problem: Understand the problem. $\newline$ We need to find the value of the logarithm of $25$ with base $7$ , which is written as $\log_7(25)$ . This means we are looking for the power to which we must raise $7$ to get $25$ .
Use Calculator or Properties: Use a calculator or logarithm properties to find the value. $\newline$ Since $25$ is not a power of $7$ , we will need to use a calculator or logarithm properties to approximate the value of $\log_{7}(25)$ . If a calculator with the ability to compute logarithms with any base is not available, we can use the change of base formula: $\newline$ $\log_{7}(25) = \frac{\log(25)}{\log(7)}$
Calculate Using Formula: Calculate using the change of base formula. $\newline$ Using a scientific calculator, we find: $\newline$ $\log(25) \approx 1.39794$ $\newline$ $\log(7) \approx 0.84510$ $\newline$ Now, divide the two values to get $\log_7(25)$ : $\newline$ $\log_7(25) \approx \frac{1.39794}{0.84510} \approx 1.654$
Round the Answer: Round the answer to the nearest thousandth. Rounding $1.654$ to the nearest thousandth gives us $1.654$ .