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Solve. Round your answer to the nearest thousandth. $\newline$ $8^x = 9$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

Full solution

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

\newline

8^x = 9

\newline

x =

____

Take Logarithm: $8^x = 9$ $\newline$ Take the logarithm of both sides of the equation to solve for $x$ . $\newline$ Apply the logarithm to both sides of $8^x = 9$ . $\newline$ $ext{log}(8^x) = ext{log}(9)$
Apply Power Property: $\log(8^x) = \log(9)$ $\newline$ Use the power property of logarithms to bring the exponent $x$ in front of the log. $\newline$ Power Property: $\log_b(M^n) = n \cdot \log_b(M)$ $\newline$ $x \cdot \log(8) = \log(9)$
Isolate $x$ : $x \cdot \log(8) = \log(9)$ $\newline$ Isolate $x$ by dividing both sides of the equation by $\log(8)$ . $\newline$ $x = \frac{\log(9)}{\log(8)}$
Calculate $x$ : Calculate the value of $x$ using a calculator. $x = \frac{\log(9)}{\log(8)}$ $x \approx 1.00043407747932$ Round $x$ to the nearest thousandth. $x \approx 1.000$

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