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Solve. Round your answer to the nearest thousandth. $\newline$ $4 = 9^x$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

Full solution

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

\newline

4 = 9^x

\newline

x =

____

Apply Logarithm: $4 = 9^x$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ Take the logarithm base $10$ of both sides. $\newline$ $ext{log}(4) = ext{log}(9^x)$
Power Property: $\log(4) = \log(9^x)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the log. $\newline$ Power Property: $\log_b(M^n) = n \cdot \log_b(M)$ $\newline$ $\log(4) = x \cdot \log(9)$
Isolate $x$ : $\log(4) = x \cdot \log(9)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(9)$ . $\newline$ $x = \frac{\log(4)}{\log(9)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x = \frac{\log(4)}{\log(9)}$ $\newline$ $x \approx \frac{0.602059991}{0.954242509}$ $\newline$ $x \approx 0.630929753$ $\newline$ Round the answer to the nearest thousandth. $\newline$ $x \approx 0.631$

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