Solve. Round your answer to the nearest thousandth. 8^x = 5 x = ____

Apply Logarithm: 8^x = 5 Apply the logarithm to both sides of the equation to solve for x. log(8^x) = log(5)Use Power Property: log(8^x) = log(5) Use the power property of logarithms to bring down the exponent. x * log(8) = log(5)Isolate x: x * log(8) = log(5) Isolate x by dividing both sides of the equation by log(8). x = log(5) / log(8)Calculate x: Calculate the value of x using a calculator. x = log(5) / log(8) x ≈ 0.767527... (using a calculator) Round the answer to the nearest thousandth. x ≈ 0.768

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Solve. Round your answer to the nearest thousandth. $\newline$ $8^x = 5$ $\newline$ $x =$ ____

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Algebra 2

Solve exponential equations using common logarithms

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Q. Solve. Round your answer to the nearest thousandth.

\newline

8^x = 5

\newline

x =

____

Apply Logarithm: $8^x = 5$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ $ext{log}(8^x) = ext{log}(5)$
Use Power Property: $\log(8^x) = \log(5)$ $\newline$ Use the power property of logarithms to bring down the exponent. $\newline$ $x \cdot \log(8) = \log(5)$
Isolate $x$ : $x \cdot \log(8) = \log(5)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(8)$ . $\newline$ $x = \frac{\log(5)}{\log(8)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x = \frac{\log(5)}{\log(8)}$ $\newline$ $x \approx 0.767527...$ (using a calculator) $\newline$ Round the answer to the nearest thousandth. $\newline$ $x \approx 0.768$