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Solve. Round your answer to the nearest thousandth. $\newline$ $5 = 7^x$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

Full solution

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

\newline

5 = 7^x

\newline

x =

____

Apply Logarithm: $5 = 7^x$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ Take the natural logarithm $(\ln)$ of both sides. $\newline$ $\ln(5) = \ln(7^x)$
Use Power Property: $\ln(5) = \ln(7^x)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the logarithm. $\newline$ Power Property: $\ln(M^n) = n \cdot \ln(M)$ $\newline$ $\ln(5) = x \cdot \ln(7)$
Isolate $x$ : $\ln(5) = x \times \ln(7)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\ln(7)$ . $\newline$ $x = \frac{\ln(5)}{\ln(7)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x = \frac{\ln(5)}{\ln(7)}$ $\newline$ $x \approx \frac{0.827087}{1.945910}$ $\newline$ $x \approx 0.424837$ $\newline$ Round the answer to the nearest thousandth. $\newline$ $x \approx 0.425$

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