Exponential inequality

Problem

Solve the inequality $2^{x^2-1} < 16.$

Solution

Write $16 = 2^4$, obtaining $2^{x^2-1} < 2^4$. The base is $2 > 1$, so the function is increasing and the direction is preserved: $x^2 - 1 < 4 \iff x^2 < 5 \iff \boxed{-\sqrt{5} < x < \sqrt{5}}.$

Links

Topics: Exponential function
Concepts: Monotonicity
Functions: Exponential function
Skills: Solving inequalities
Exercise type: Solving an inequality