10 December 2021

Statement

Solve the following equation for \(x\).

\(2^{x-5} = 3\).

Solution

\(2^{x-5} = 3\)

We start by applying the \(log_{2}\) on both sides of the equation.
Since both sides are positive it is safe to apply this operation.

\(\Leftrightarrow log_{2}{2^{x-5}} = log_{2}{3} \)

\(\Leftrightarrow x-5 = log_{2}{3} \)

\(\Leftrightarrow x = log_{2}{3} + 5 \)