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Solve. Round your answer to the nearest thousandth. $\newline$ $6 = 5^x$ $\newline$ $x =$ ____

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Solve exponential equations using logarithms

Full solution

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

\newline

6 = 5^x

\newline

x =

____

Apply Logarithm: Apply the logarithm to both sides of the equation $6 = 5^x$ to make the exponent $x$ solvable. $\newline$ $\log(6) = \log(5^x)$
Use Power Property: Use the power property of logarithms to bring the exponent $x$ in front of the log on the right side of the equation. $\log(6) = x \cdot \log(5)$
Isolate $x$ : Isolate $x$ by dividing both sides of the equation by $\log(5)$ . $x = \frac{\log(6)}{\log(5)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x = \frac{\log(6)}{\log(5)}$ $\newline$ $x = \frac{0.7781512504}{0.6989700043}$ $\newline$ $x = 1.113282752$
Round to Nearest: Round the value of $x$ to the nearest thousandth. $x \approx 1.113$

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