Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 307: 78

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

We have: $e^{3x}=e^{2-x}$ Use the power rule: $a^p=a^q$. We can see that the base $a=e$ is the same on both sides of the equation. So, the exponents will also be equal. This implies that $p=q$ Therefore, $3x=2-x \\ 3x+x=2 \\ 4x=2 \\ x=\dfrac{1}{2}$