EXPONENTIAL FUNCTIONS Solving Exponential Inequalities (Page 1 of 2)

Solving an exponential inequality is nearly the same as solving an equation. In fact, we solve the equation first using the x-intercept method, then analyze the graph to determine the solution set of the inequality.

To solve the inequality 3^(2x+1) > 5^(x+2), we first get a zero on the right: 3^(2x+1)-5^(x+2) > 0. Then replace the inequality symbol with an equal sign: 3^(2x+1)-5^(x+2) = 0. This equation was solved in a previous example using CALC zero and the solution was determined to be x ≈ 3.607. The graph of the function represented by the left side of the equation, f(x) = 3^(2x+1)-5^(x+2), is shown along with the zero.

GRAPH key. Calculator screen image.
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