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Solve. Round your answer to the nearest thousandth. $\newline$ $2 = 5^x$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

Full solution

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

\newline

2 = 5^x

\newline

x =

____

Apply Logarithm: $2 = 5^x$ $\newline$ Apply the logarithm to both sides of the equation to solve for $x$ . $\newline$ $\log(2) = \log(5^x)$
Power Property: $\log(2) = \log(5^x)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the log. $\newline$ $\log(2) = x \cdot \log(5)$
Isolate $x$ : $\log(2) = x \cdot \log(5)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(5)$ . $\newline$ $x = \frac{\log(2)}{\log(5)}$
Calculate $x$ : Calculate the value of $x$ using a calculator. $\newline$ $x = \frac{\log(2)}{\log(5)}$ $\newline$ $x \approx 0.430676558...$ (using a calculator) $\newline$ Round $x$ to the nearest thousandth. $\newline$ $x \approx 0.431$

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