# Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 404: 42

$x=\frac{1}{2}$

#### Work Step by Step

We need to solve: $3^{4x}-3^{2x}-6=0$ We factor: $(3^{2x}-3)(3^{2x}+2)=0$ $(3^{2x}-3)=0$ or $(3^{2x}+2)=0$ $3^{2x}=3$ or $3^{2x}=-2$ $2x=\log_3 3=1$ or $2x=\log_3 -2$=no solution $2x=1$ $x=\frac{1}{2}$

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