Solve. Round your answer to the nearest thousandth. 5 = 6^x x = ____

Apply Logarithms: 5 = 6^x Apply logarithms to both sides of the equation to solve for x. Take the natural logarithm (ln) of both sides. ln(5) = ln(6^x)Use Power Property: ln(5) = ln(6^x) Use the power property of logarithms to bring the exponent x in front of the logarithm. Power Property: ln(a^b) = b * ln(a) ln(5) = x * ln(6)Isolate x: ln(5) = x * ln(6) Isolate x by dividing both sides of the equation by ln(6). x = ln(5) / ln(6)Calculate x: Calculate the value of x using a calculator. x = ln(5) / ln(6) x ≈ 0.898 / 1.792 x ≈ 0.501 Round the answer to the nearest thousandth. x ≈ 0.501

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Solve for $x$ . $\newline$ $5 = 6^x$ $\newline$ 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

5 = 6^x

\newline

Round your answer to the nearest thousandth.

Apply Logarithms: $5 = 6^x$ $\newline$ Apply logarithms to both sides of the equation to solve for $x$ . $\newline$ Take the natural logarithm $(\ln)$ of both sides. $\newline$ $\ln(5) = \ln(6^x)$
Use Power Property: $\ln(5) = \ln(6^x)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the logarithm. $\newline$ Power Property: $\ln(a^b) = b \cdot \ln(a)$ $\newline$ $\ln(5) = x \cdot \ln(6)$
Isolate $x$ : $\ln(5) = x \cdot \ln(6)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\ln(6)$ . $\newline$ $x = \frac{\ln(5)}{\ln(6)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x = \frac{\ln(5)}{\ln(6)}$ $\newline$ $x \approx \frac{0.898}{1.792}$ $\newline$ $x \approx 0.501$ $\newline$ Round the answer to the nearest thousandth. $\newline$ $x \approx 0.501$