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

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Solve exponential equations using common logarithms

Full solution

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

\newline

7 = 2^x

\newline

x =

____

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. $x \approx 4.047$

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