Solve. Round your answer to the nearest thousandth. 7 = 8^x x = ____

Write Equation: Write down the equation. We have the equation 7 = 8^x.Apply Logarithm: Apply the logarithm to both sides of the equation. Taking the logarithm of both sides gives us log(7) = log(8^x).Use Power Property: Use the power property of logarithms. The power property of logarithms states that log(a^b) = b * log(a). Applying this to our equation gives us log(7) = x * log(8).Isolate Variable x: Isolate the variable x. To solve for x, we divide both sides by log(8), which gives us x = log(7) / log(8).Calculate with Calculator: Calculate the value of x using a calculator. Using a calculator, we find that log(7) ≈ 0.845098040 and log(8) ≈ 0.903089987. Therefore, x ≈ 0.845098040 / 0.903089987.Perform Division: Perform the division to find the value of x. After dividing, we get x ≈ 0.935507576.Round to Nearest Thousandth: Round the answer to the nearest thousandth. Rounding 0.935507576 to the nearest thousandth gives us x ≈ 0.936.

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Solve. Round your answer to the nearest thousandth. $\newline$ $7 = 8^x$ $\newline$ $x =$ ____

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Precalculus

Solve exponential equations using logarithms

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

\newline

7 = 8^x

\newline

x =

____

Write Equation: Write down the equation. $\newline$ We have the equation $7 = 8^x$ .
Apply Logarithm: Apply the logarithm to both sides of the equation. $\newline$ Taking the logarithm of both sides gives us $\log(7) = \log(8^x)$ .
Use Power Property: Use the power property of logarithms. $\newline$ The power property of logarithms states that $\log(a^b) = b \cdot \log(a)$ . Applying this to our equation gives us $\log(7) = x \cdot \log(8)$ .
Isolate Variable x: Isolate the variable $x$ .\ To solve for $x$ , we divide both sides by $\log(8)$ , which gives us $x = \frac{\log(7)}{\log(8)}$ .
Calculate with Calculator: Calculate the value of $x$ using a calculator. $\newline$ Using a calculator, we find that $\log(7) \approx 0.845098040$ and $\log(8) \approx 0.903089987$ . Therefore, $x \approx \frac{0.845098040}{0.903089987}$ .
Perform Division: Perform the division to find the value of $x$ . $\newline$ After dividing, we get $x \approx 0.935507576$ .
Round to Nearest Thousandth: Round the answer to the nearest thousandth. $\newline$ Rounding $0.935507576$ to the nearest thousandth gives us $x \approx 0.936$ .