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Solve. Round your answer to the nearest thousandth. $\newline$ $7 = 6^x$ $\newline$ $x =$ ____

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Solve exponential equations using common logarithms

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

\newline

7 = 6^x

\newline

x =

____

Understand and Apply Logarithms: Understand the equation and apply logarithms. $\newline$ We have the equation $7 = 6^x$ . To solve for $x$ , we can apply logarithms to both sides of the equation. $\newline$ Take the logarithm of both sides: $\newline$ $log(7) = log(6^x)$
Use Power Property of Logarithms: Use the power property of logarithms. The power property of logarithms states that $\log_b(M^n) = n \cdot \log_b(M)$ . We can use this property to simplify the right side of the equation: $\log(7) = x \cdot \log(6)$
Isolate x: Isolate $x$ . $\newline$ To solve for $x$ , we need to isolate it on one side of the equation. We can do this by dividing both sides by $\log(6)$ : $\newline$ $x = \frac{\log(7)}{\log(6)}$
Calculate x Value: Calculate the value of x. $\newline$ Using a calculator, we find the values of $\log(7)$ and $\log(6)$ and then divide them to find $x$ : $\newline$ $x = \frac{\log(7)}{\log(6)}$ $\newline$ $x \approx \frac{1.20906}{0.77815}$ $\newline$ $x \approx 1.553$

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