Solve. Round your answer to the nearest thousandth. 5^x = 2 x = ____

Apply Logarithm: 5^x = 2 Apply the logarithm to both sides of the equation to solve for x. log(5^x) = log(2)Use Power Property: log(5^x) = log(2) Use the power property of logarithms to bring the exponent x in front of the log. x * log(5) = log(2)Isolate x: x * log(5) = log(2) Isolate x by dividing both sides of the equation by log(5). x = log(2) / log(5)Calculate x: x = log(2) / log(5) Calculate the value of x using a calculator. x ≈ log(2) / log(5) x ≈ 0.43067655807339306...Round to Nearest Thousandth: Round the value of x to the nearest thousandth. x ≈ 0.431

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Solve. Round your answer to the nearest thousandth. $\newline$ $5^x = 2$ $\newline$ $x =$ ____

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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

5^x = 2

\newline

x =

____

Apply Logarithm: $5^x = 2$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ $ext{log}(5^x) = ext{log}(2)$
Use Power Property: $\log(5^x) = \log(2)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the log. $\newline$ $x \cdot \log(5) = \log(2)$
Isolate $x$ : $x \cdot \log(5) = \log(2)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(5)$ . $\newline$ $x = \frac{\log(2)}{\log(5)}$
Calculate $x$ : $x = \frac{\log(2)}{\log(5)}$ $\newline$ Calculate the value of $x$ using a calculator. $\newline$ $x \approx \frac{\log(2)}{\log(5)}$ $\newline$ $x \approx 0.43067655807339306\ldots$
Round to Nearest Thousandth: Round the value of $x$ to the nearest thousandth. $x \approx 0.431$