Equation with passage to the exponential

Statement

Solve $\log_2(x^2 - 1) = 3$.

Solution

EC: $x^2 - 1 > 0 \iff x < -1 \vee x > 1$.

Passing to the exponential: $x^2 - 1 = 2^3 = 8 \iff x^2 = 9 \iff x = \pm 3$.

EC check: both $x = 3$ and $x = -3$ satisfy $x^2 - 1 > 0$.

Solutions: $\boxed{x = \pm 3}$.

Links

Topics: Logarithmic function
Concepts: Existence conditions · Logarithmic equations · Logarithm
Functions: Logarithmic function
Methods: Logarithm equations
Skills: Solve equations
Exercise type: Solving an equation