Solving Exponential Equations

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

To solve exponential equations with the same base, set the exponents equal to each other. For example, if 3^x = 3^4, then x = 4.

The first step is to recognize that both sides of the equation have the same base (3), allowing you to set the exponents equal: 3 = 4x + 2.

x = 1/4.

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, 2^-3 = 1/(2^3) = 1/8.

Set the exponents equal: -m = 3m - 3, then solve for m.

m = 3/4.

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

n = -3.

Any non-zero base raised to the power of zero equals one: a^0 = 1.