Solve. Round your answer to the nearest thousandth. 7 = 2^x x = ____

Understand and Apply Logarithms: Understand the equation and apply logarithms. We have the equation 7 = 2^x. To solve for x, we will apply logarithms to both sides of the equation. Take the logarithm of both sides: log(7) = log(2^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(7) = x * log(2)Isolate x: Isolate x. To solve for x, we need to isolate it on one side of the equation. x = log(7) / log(2)Calculate x: Calculate the value of x using a calculator. Using a calculator, we find the values of log(7) and log(2) and then divide them to find x. x = log(7) / log(2) ≈ 2.807354922057604 / 0.6931471805599453 ≈ 4.047189562170502Round to Nearest Thousandth: Round the answer to the nearest thousandth. x ≈ 4.047

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Solve for $x$ . $\newline$ $7 = 2^x$ $\newline$ 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

7 = 2^x

\newline

Round your answer to the nearest thousandth.

Understand and Apply Logarithms: Understand the equation and apply logarithms. $\newline$ We have the equation $7 = 2^x$ . To solve for $x$ , we will apply logarithms to both sides of the equation. $\newline$ Take the logarithm of both sides: $\newline$ $log(7) = log(2^x)$
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. $\log(7) = x \cdot \log(2)$
Isolate x: Isolate $x$ . $\newline$ To solve for $x$ , we need to isolate it on one side of the equation. $\newline$ $x = \frac{\log(7)}{\log(2)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ Using a calculator, we find the values of $\log(7)$ and $\log(2)$ and then divide them to find x. $\newline$ $x = \frac{\log(7)}{\log(2)} \approx \frac{2.807354922057604}{0.6931471805599453} \approx 4.047189562170502$
Round to Nearest Thousandth: Round the answer to the nearest thousandth. $x \approx 4.047$