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

Apply Logarithm: 2 = 5^x Apply the logarithm to both sides of the equation to solve for x. log(2) = log(5^x)Power Property: log(2) = log(5^x) Use the power property of logarithms to bring the exponent x in front of the log. log(2) = x * log(5)Isolate x: log(2) = x * log(5) Isolate x by dividing both sides of the equation by log(5). x = log(2) / log(5)Calculate x: Calculate the value of x using a calculator. x = log(2) / log(5) x ≈ 0.430676558... (using a calculator) Round x to the nearest thousandth. x ≈ 0.431

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

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Algebra 2

Solve exponential equations using common logarithms

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Q. Solve for

x

\newline

2 = 5^x

\newline

Round your answer to the nearest thousandth.

Apply Logarithm: $2 = 5^x$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ $\log(2) = \log(5^x)$
Power Property: $\log(2) = \log(5^x)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the log. $\newline$ $\log(2) = x \cdot \log(5)$
Isolate $x$ : $\log(2) = x \cdot \log(5)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(5)$ . $\newline$ $x = \frac{\log(2)}{\log(5)}$
Calculate $x$ : Calculate the value of $x$ using a calculator. $\newline$ $x = \frac{\log(2)}{\log(5)}$ $\newline$ $x \approx 0.430676558...$ (using a calculator) $\newline$ Round $x$ to the nearest thousandth. $\newline$ $x \approx 0.431$