Chapter 4 - Section 4.2 - Exponential Functions - 4.2 Exercises - Page 412: 103

These are: $x\approx1.3$ and $x=-0.5$

Here, we have to graph functions on the two sides of the equation. $3x+2=4^x$ So by graphing the functions $f(x)=3x+2$ (in blue) and $g(x)=4^x$ (in green), we can see that, there are two intersection points, therefore there will be two solutions. These are: $x\approx1.3$ and $x=-0.5$