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Solve. Round your answer to the nearest thousandth. $\newline$ $7^x = 4$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

Full solution

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

\newline

7^x = 4

\newline

x =

____

Apply Logarithm: $7^x = 4$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ $log(7^x) = log(4)$
Power Property: $\log(7^x) = \log(4)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the log. $\newline$ $x \cdot \log(7) = \log(4)$
Isolate $x$ : $x \cdot \log(7) = \log(4)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(7)$ . $\newline$ $x = \frac{\log(4)}{\log(7)}$
Calculate $x$ : $x = \frac{\log(4)}{\log(7)}$ $\newline$ Calculate the value of $x$ using a calculator. $\newline$ $x \approx \frac{\log(4)}{\log(7)}$ $\newline$ $x \approx \frac{0.602059991}{0.845098040}$ $\newline$ $x \approx 0.712414$
Round to Nearest Thousandth: Round the value of $x$ to the nearest thousandth. $x \approx 0.712$

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