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Solve. Round your answer to the nearest thousandth. $\newline$ $3 = 2^x$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

Full solution

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

\newline

3 = 2^x

\newline

x =

____

Apply Logarithm: $3 = 2^x$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ $ext{log}(3) = ext{log}(2^x)$
Use Power Property: $\log(3) = \log(2^x)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the log. $\newline$ $\log(3) = x \cdot \log(2)$
Isolate $x$ : $\log(3) = x \cdot \log(2)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(2)$ . $\newline$ $x = \frac{\log(3)}{\log(2)}$
Calculate $x$ : Calculate the value of $x$ using a calculator. $\newline$ $x = \frac{\log(3)}{\log(2)}$ $\newline$ $x \approx 1.58496250072\dots$ $\newline$ Round $x$ to the nearest thousandth. $\newline$ $x \approx 1.585$

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