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

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Solve exponential equations using common logarithms

Full solution

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

\newline

2 = 9^x

\newline

x =

____

Understand and Apply Logarithms: Understand the equation and apply logarithms. $\newline$ We have the equation $2 = 9^x$ . To solve for $x$ , we will apply logarithms to both sides of the equation. $\newline$ Take the logarithm of both sides: $\newline$ $log(2) = log(9^x)$
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 will apply this property to simplify the equation. $\log(2) = x \cdot \log(9)$
Isolate x: Isolate $x$ . $\newline$ To solve for $x$ , we need to isolate it on one side of the equation. $\newline$ $x = \frac{\log(2)}{\log(9)}$
Calculate x Value: Calculate the value of x using a calculator. $\newline$ Now we will use a calculator to find the value of x. $\newline$ $x = \frac{\log(2)}{\log(9)} \approx 0.31546487\ldots$
Round to Nearest Thousandth: Round the answer to the nearest thousandth. $\newline$ Round the calculated value of $x$ to three decimal places. $\newline$ $x \approx 0.315$

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