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Solve. Round your answer to the nearest thousandth. $\newline$ $8^x = 3$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

Full solution

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

\newline

8^x = 3

\newline

x =

____

Apply Logarithm: $8^x = 3$ $\newline$ Apply the logarithm to both sides of the equation to solve for x. $\newline$ $log(8^x) = log(3)$
Use Power Property: $\log(8^x) = \log(3)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the log. $\newline$ $x \cdot \log(8) = \log(3)$
Isolate $x$ : $x \cdot \log(8) = \log(3)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(8)$ . $\newline$ $x = \frac{\log(3)}{\log(8)}$
Calculate $x$ : Calculate the value of $x$ using a calculator. $\newline$ $x = \frac{\log(3)}{\log(8)}$ $\newline$ $x \approx 0.5283208336\ldots$
Round $x$ : Round the value of $x$ to the nearest thousandth. $x \approx 0.528$

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