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

Identify Equation: Identify the equation to solve. We are given the equation 4^x = 9 and we need to find the value of x.Apply Logarithms: Apply logarithms to both sides of the equation. To solve for x, we can take the logarithm of both sides of the equation. We can use any logarithm, but for simplicity, we'll use the natural logarithm (ln). ln(4^x) = ln(9)Use Power Property: Use the power property of logarithms. The power property of logarithms states that ln(a^b) = b*ln(a). We apply this property to simplify the left side of the equation. x*ln(4) = ln(9)Isolate x: Isolate x. To solve for x, we divide both sides of the equation by ln(4). x = ln(9) / ln(4)Calculate Value: Calculate the value of x using a calculator. Using a calculator, we find: x = ln(9) / ln(4) x ≈ 2.197224577 / 1.386294361 x ≈ 1.584962501Round Answer: Round the answer to the nearest thousandth. x ≈ 1.585

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

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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

4^x = 9

\newline

x =

____

Identify Equation: Identify the equation to solve. $\newline$ We are given the equation $4^x = 9$ and we need to find the value of $x$ .
Apply Logarithms: Apply logarithms to both sides of the equation. $\newline$ To solve for $x$ , we can take the logarithm of both sides of the equation. We can use any logarithm, but for simplicity, we'll use the natural logarithm (ln). $\newline$ $\ln(4^x) = \ln(9)$
Use Power Property: Use the power property of logarithms. $\newline$ The power property of logarithms states that $\ln(a^b) = b\cdot\ln(a)$ . We apply this property to simplify the left side of the equation. $\newline$ $x\cdot\ln(4) = \ln(9)$
Isolate x: Isolate $x$ . $\newline$ To solve for $x$ , we divide both sides of the equation by $\ln(4)$ . $\newline$ $x = \frac{\ln(9)}{\ln(4)}$
Calculate Value: Calculate the value of $x$ using a calculator. $\newline$ Using a calculator, we find: $\newline$ $x = \frac{\ln(9)}{\ln(4)}$ $\newline$ $x \approx \frac{2.197224577}{1.386294361}$ $\newline$ $x \approx 1.584962501$
Round Answer: Round the answer to the nearest thousandth. $x \approx 1.585$