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Solve. Round your answer to the nearest thousandth. $\newline$ $9^x = 2$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

Full solution

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

\newline

9^x = 2

\newline

x =

____

Apply Logarithm: $9^x = 2$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ $ext{log}(9^x) = ext{log}(2)$
Power Property: $\log(9^x) = \log(2)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the log. $\newline$ $x \cdot \log(9) = \log(2)$
Isolate $x$ : $x \cdot \log(9) = \log(2)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(9)$ . $\newline$ $x = \frac{\log(2)}{\log(9)}$
Calculate $x$ : $x = \frac{\log(2)}{\log(9)}$ $\newline$ Calculate the value of $x$ using a calculator. $\newline$ $x \approx \frac{\log(2)}{\log(9)}$ $\newline$ $x \approx 0.6309297535714574\ldots$
Round to Nearest: Round the value of $x$ to the nearest thousandth. $x \approx 0.631$

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