Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.1 Exponential And Logarithmic Functions - Exercises Set 6.1 - Page 419: 22

$$x = \root 5 \of 2 $$

$$\eqalign{ & \ln 4x - 3\ln \left( {{x^2}} \right) = \ln 2 \cr & {\text{use the power property for logarithms }}\log {a^n} = n\log a \cr & \ln 4x - \ln \left( {{x^6}} \right) = \ln 2 \cr & {\text{use the quotient property for logarithms}} \cr & \ln \left( {\frac{{4x}}{{{x^6}}}} \right) = \ln 2 \cr & {\text{simplify}} \cr & \ln \left( {\frac{4}{{{x^5}}}} \right) = \ln 2 \cr & {\text{then}}{\text{,}} \cr & \frac{4}{{{x^5}}} = 2 \cr & {x^5} = 2 \cr & x = \root 5 \of 2 \cr} $$