Manipulating the Equation The equation given is 5 to the power x minus 3 to the power x equals 16. To solve this, we can divide everything by 5 to the power x and get a decreasing function on one side of an equation and an increasing function on another.

Finding Solutions Another approach is adding both sides with a constant value which results in two decreasing functions that intersect at only one point. The original problem has only one solution, which can be found using guess-and-check method as x=2.