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

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Solve exponential equations using common logarithms

Full solution

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

\newline

5 = 6^x

\newline

x =

____

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. $\newline$ $x \approx 0.501$

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