Solve. Round your answer to the nearest thousandth. 5 = 4^x x = ____

Understand and Apply Logarithms: Understand the equation and apply logarithms. We have the equation 5 = 4^x. To solve for x, we can apply logarithms to both sides of the equation. log(5) = log(4^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 can apply this property to simplify the equation. log(5) = x * log(4)Isolate x: Isolate x. To solve for x, we need to isolate it on one side of the equation. x = log(5) / log(4)Calculate x Using Calculator: Calculate the value of x using a calculator. Using a calculator, we find the values of log(5) and log(4), then divide them to find x. x = log(5) / log(4) x ≈ 1.16096404744 / 0.60205999132 x ≈ 1.924Round to Nearest Thousandth: Round the answer to the nearest thousandth. x ≈ 1.924 rounded to the nearest thousandth is 1.924.

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Solve for $x$ . $\newline$ $5 = 4^x$ $\newline$ Round your answer to the nearest thousandth.

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Algebra 2

Solve exponential equations using common logarithms

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Q. Solve for

x

\newline

5 = 4^x

\newline

Round your answer to the nearest thousandth.

Understand and Apply Logarithms: Understand the equation and apply logarithms. $\newline$ We have the equation $5 = 4^x$ . To solve for $x$ , we can apply logarithms to both sides of the equation. $\newline$ $\log(5) = \log(4^x)$
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. $\log(5) = x \cdot \log(4)$
Isolate $x$ : Isolate $x$ . $\newline$ To solve for $x$ , we need to isolate it on one side of the equation. $\newline$ $x = \frac{\log(5)}{\log(4)}$
Calculate x Using Calculator: Calculate the value of x using a calculator. $\newline$ Using a calculator, we find the values of $\log(5)$ and $\log(4)$ , then divide them to find x. $\newline$ $x = \frac{\log(5)}{\log(4)}$ $\newline$ $x \approx \frac{1.16096404744}{0.60205999132}$ $\newline$ $x \approx 1.924$
Round to Nearest Thousandth: Round the answer to the nearest thousandth. $\newline$ $x \approx 1.924$ rounded to the nearest thousandth is $1.924$ .