Chapter 7 Exponential and Logarithmic Functions - 7.6 Solve Exponential and Logarithmic Equations - Guided Practice for Examples 4, 5, and 6 - Page 518: 10

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Using the rules of logarithms to solve the equation, we find: $$\log _4\left(\left(x+12\right)x\right)=3 \\ \log _4\left(\left(x+12\right)x\right)=\log _4\left(64\right) \\ \left(x+12\right)x=64 \\ x=4,\:x=-16$$ Checking for extraneous solutions, we see that only $x=4$ is valid.