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Solve. Round your answer to the nearest thousandth. $\newline$ $5 = 9^x$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

Full solution

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

\newline

5 = 9^x

\newline

x =

____

Understand and Apply Logarithms: Understand the equation and apply logarithms. $\newline$ We have the equation $5 = 9^x$ . To solve for $x$ , we can apply logarithms to both sides of the equation. $\newline$ $\log(5) = \log(9^x)$
Use Power Property of Logarithms: Use the power property of logarithms. The power property of logarithms states that $\log_b(M^n) = n \cdot \log_b(M)$ . We can apply this property to simplify the equation. $\log(5) = x \cdot \log(9)$
Isolate $x$ : Isolate $x$ . $\newline$ To solve for $x$ , we need to isolate it on one side of the equation. $\newline$ $x = \frac{\log(5)}{\log(9)}$
Calculate x Value: Calculate the value of x using a calculator. $\newline$ Using a calculator, we find the values of $\log(5)$ and $\log(9)$ and then divide them to find x. $\newline$ $x = \frac{\log(5)}{\log(9)} \approx \frac{0.69897}{0.95424} \approx 0.732$
Round to Nearest Thousandth: Round the answer to the nearest thousandth. $\newline$ The calculated value of $x$ is approximately $0.732$ , which is already rounded to the nearest thousandth.

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