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Solve. Round your answer to the nearest thousandth. $\newline$ $2^x = 5$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

Full solution

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

\newline

2^x = 5

\newline

x =

____

Apply Logarithm: $2^x = 5$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ $ext{log}(2^x) = ext{log}(5)$
Use Power Property: $\log(2^x) = \log(5)$ $\newline$ Use the power property of logarithms to bring down the exponent. $\newline$ $x \cdot \log(2) = \log(5)$
Isolate $x$ : $x \cdot \log(2) = \log(5)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(2)$ . $\newline$ $x = \frac{\log(5)}{\log(2)}$
Calculate $x$ : Calculate the value of $x$ using a calculator. $x = \frac{\log(5)}{\log(2)}$ $x \approx \frac{2.32192809}{0.69314718}$ $x \approx \frac{3.321928094887362}{0.6931471805599453}$ $x \approx 2.321928094887362$
Round to Nearest Thousandth: Round the value of $x$ to the nearest thousandth. $x \approx 2.322$

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