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

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Solve exponential equations using common logarithms

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

\newline

5 = 4^x

\newline

x =

____

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 $1.924$ .

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