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

Write Equation: Write down the equation that needs to be solved. We have the equation 9 = 2^x.Apply Logarithm: Apply the logarithm to both sides of the equation to solve for x. 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. The power property of logarithms states that log(a^b) = b * log(a). Therefore, log(9) = x * log(2).Isolate x: Isolate x by dividing both sides of the equation by log(2). We get x = log(9) / log(2).Calculate Value: Calculate the value of x using a calculator. Using a calculator, we find x = log(9) / log(2) ≈ 3.169925001 / 0.693147181 = 4.573.Round Answer: Round the answer to the nearest thousandth. The rounded value of x is x ≈ 4.573.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

Home

Math Problems

Precalculus

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 $x \approx 4.573$ .