Exponential Equations (no logs)

An exponential equation is an equation in which a variable appears in the exponent. For example, $$2^x = 8$$ .

To solve exponential equations, you typically need to rewrite both sides of the equation with the same base, then set the exponents equal to each other.

The base is the number that is raised to a power in an exponential expression. For example, in $$2^x$$ , 2 is the base.

Having like bases means that both sides of the equation can be expressed with the same base, allowing you to equate the exponents.

8 can be rewritten as $$2^3$$ .

The solution is $$p = 1$$ .

The value of $$x$$ is $$\frac{1}{4}$$ .

The solution is $$x = 7$$ .

The first step is to rewrite 8 as $$2^3$$ .

If $$a^m = a^n$$ , then $$m = n$$ , provided that $$a$$ is not zero.