Chapter 7 Exponential and Logarithmic Functions - 7.6 Solve Exponential and Logarithmic Equations - 7.6 Exercises - Skill Practice - Page 520: 35

35.6

Using the rules of logarithms to solve the equation, we find: $$\log _4\left(2x\right)=\frac{40}{13} \\ \log _4\left(2x\right)=\log _4\left(64\cdot \:4^{\frac{1}{13}}\right) \\ x=32\cdot \:4^{\frac{1}{13}} \\ x=35.6$$ Checking for extraneous solutions, we see that the given solution is valid.