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

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Solve exponential equations using common logarithms

Full solution

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

\newline

5^x = 8

\newline

x =

____

Apply Logarithm: $5^x = 8$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ $ext{log}(5^x) = ext{log}(8)$
Use Power Property: $\log(5^x) = \log(8)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the log. $\newline$ $x \cdot \log(5) = \log(8)$
Isolate $x$ : $x \cdot \log(5) = \log(8)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(5)$ . $\newline$ $x = \frac{\log(8)}{\log(5)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x = \frac{\log(8)}{\log(5)}$ $\newline$ $x \approx \frac{1.292029674}{0.698970004}$ $\newline$ $x \approx 1.849$

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