Systems of exponential equations and inequalities

A system of exponential equations or inequalities is a set of two or more equations or inequalities where the variable appears in the exponent. Solving such systems usually involves rewriting the equations to have the same base, using properties of exponents, or applying logarithms to isolate the variable.

Important properties

• If the bases are the same and the expressions are equal, then the exponents must be equal.

• Exponential functions are always positive for real bases greater than 0 and not equal to 1.

• Logarithms can be used to solve for variables in exponents.

• Systems may have one, many, or no solutions, depending on the equations.