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Solve. Round your answer to the nearest thousandth. $\newline$ $8^x = 5$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

Full solution

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

\newline

8^x = 5

\newline

x =

____

Apply Logarithm: $8^x = 5$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ $ext{log}(8^x) = ext{log}(5)$
Use Power Property: $\log(8^x) = \log(5)$ $\newline$ Use the power property of logarithms to bring down the exponent. $\newline$ $x \cdot \log(8) = \log(5)$
Isolate $x$ : $x \cdot \log(8) = \log(5)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(8)$ . $\newline$ $x = \frac{\log(5)}{\log(8)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x = \frac{\log(5)}{\log(8)}$ $\newline$ $x \approx 0.767527...$ (using a calculator) $\newline$ Round the answer to the nearest thousandth. $\newline$ $x \approx 0.768$

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