10 December 2021

Statement

Solve the following equation for \(x\).

\(e^{7-4x} = 6\).

Solution

\(e^{7-4x} = 6\)

We start by applying the \(\ln\) on both sides of the equation.
Since both sides are positive it is okay to apply this operation.

\(\Leftrightarrow \ln{e^{7-4x}} = \ln{6}\)

\(\Leftrightarrow 7 - 4x = \ln{6}\)

\(\Leftrightarrow 4x = 7 - \ln{6}\)

\(\Leftrightarrow x = \frac{7 - \ln{6}}{4}\)