Solve. Round your answer to the nearest thousandth. 4^x = 7 x = ____

Write Equation: Write down the equation. We have the equation 4^x = 7. We need to solve for x.Apply Logarithms: Apply logarithms to both sides of the equation. Taking the logarithm of both sides gives us log(4^x) = log(7).Use Power Property: Use the power property of logarithms. The power property of logarithms states that log_b(M^n) = n * log_b(M). Therefore, we can write x * log(4) = log(7).Isolate x: Isolate x. To solve for x, we divide both sides by log(4), which gives us x = log(7) / log(4).Calculate x: Calculate the value of x using a calculator. x = log(7) / log(4) ≈ 1.403 / 0.602 ≈ 2.330Round Answer: Round the answer to the nearest thousandth. x ≈ 2.330

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Solve. Round your answer to the nearest thousandth. $\newline$ $4^x = 7$ $\newline$ $x =$ ____

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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 = 7

\newline

x =

____

Write Equation: Write down the equation. $\newline$ We have the equation $4^x = 7$ . $\newline$ We need to solve for $x$ .
Apply Logarithms: Apply logarithms to both sides of the equation. $\newline$ Taking the logarithm of both sides gives us $\log(4^x) = \log(7)$ .
Use Power Property: Use the power property of logarithms. The power property of logarithms states that $\log_b(M^n) = n \cdot \log_b(M)$ . Therefore, we can write $x \cdot \log(4) = \log(7)$ .
Isolate $x$ : Isolate $x$ . $\newline$ To solve for $x$ , we divide both sides by $\log(4)$ , which gives us $x = \frac{\log(7)}{\log(4)}$ .
Calculate x: Calculate the value of x using a calculator. $\newline$ $x = \frac{\log(7)}{\log(4)} \approx \frac{1.403}{0.602} \approx 2.330$
Round Answer: Round the answer to the nearest thousandth. $x \approx 2.330$