Exponential equations

An exponential equation is an equation in which the variable appears in the exponent, such as $2^x = 8$ or $3^{2x+1} = 27$. To solve these equations, we often rewrite both sides so they have the same base, or use properties of exponents.

Important properties

• If $a^x = a^y$ and $a > 0$, $a \neq 1$, then $x = y$.

• Exponential equations can often be solved by expressing both sides with the same base.

• Sometimes, substitution or factoring can help solve more complex exponential equations.