Solve Exponential Equations

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

The general form of an exponential function is $$f(x) = a \times b^x$$ , where $$a$$ is a constant, $$b$$ is the base (a positive real number), and $$x$$ is the exponent.

Any non-zero number raised to the power of 0 is equal to 1. For example, $$15^0 = 1$$ .

Since the bases are the same, set the exponents equal: $$3 = 4x + 2$$ . Solving gives $$x = \frac{1}{4}$$ .

Rewrite 36 as a power of 6: $$36 = 6^2$$ , then set the exponents equal: $$2 = x$$ .

The base of the exponential function $$f(x) = 2^x$$ is 2.

$$64 = 4^3$$ .

Rewrite 64 as a power of 4: $$64 = 4^3$$ . Set the exponents equal: $$p + 2 = 3$$ , so $$p = 1$$ .

This property states that when multiplying two exponential expressions with the same base, you can add the exponents.

This property states that when dividing two exponential expressions with the same base, you can subtract the exponents.