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

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

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

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Algebra 2

Solve exponential equations using common logarithms

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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. $\newline$ $x \approx 0.315$