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Solve. Round your answer to the nearest thousandth. $\newline$ $7 = 3^x$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

Full solution

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

\newline

7 = 3^x

\newline

x =

____

Apply Logarithm: $7 = 3^x$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ Take the natural logarithm $(\ln)$ of both sides. $\newline$ $\ln(7) = \ln(3^x)$
Use Power Property: $\ln(7) = \ln(3^x)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the logarithm. $\newline$ Power Property: $\ln(a^b) = b \cdot \ln(a)$ $\newline$ $\ln(7) = x \cdot \ln(3)$
Isolate $x$ : $\ln(7) = x \cdot \ln(3)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\ln(3)$ . $\newline$ $x = \frac{\ln(7)}{\ln(3)}$
Calculate $x$ : Calculate the value of $x$ using a calculator. $\newline$ $x = \frac{\ln(7)}{\ln(3)}$ $\newline$ $x \approx 1.77124374916...$ $\newline$ Round the answer to the nearest thousandth. $\newline$ $x \approx 1.771$

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