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Solve. Round your answer to the nearest thousandth. $\newline$ $9 = 2^x$ $\newline$ $x =$ ____

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Solve exponential equations using logarithms

Full solution

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

\newline

9 = 2^x

\newline

x =

____

Write Equation: Write down the equation that needs to be solved. $\newline$ We have the equation $9 = 2^x$ .
Apply Logarithm: Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ Taking the logarithm of both sides, we get $\log(9) = \log(2^x)$ .
Use Power Property: Use the power property of logarithms to simplify the right side of the equation. $\newline$ The power property of logarithms states that $\log(a^b) = b \cdot \log(a)$ . Therefore, $\log(9) = x \cdot \log(2)$ .
Isolate $x$ : Isolate $x$ by dividing both sides of the equation by $\log(2)$ . We get $x = \frac{\log(9)}{\log(2)}$ .
Calculate Value: Calculate the value of $x$ using a calculator. $\newline$ Using a calculator, we find $x = \frac{\log(9)}{\log(2)} \approx \frac{3.169925001}{0.693147181} = 4.573$ .
Round Answer: Round the answer to the nearest thousandth. $\newline$ The rounded value of $x$ is $x \approx 4.573$ .

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