Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 67

Sample answer: She is probably thinking that a negative number can not be a solution to a logarithmic equation.

She is probably thinking that a negative number can not be a solution to a logarithmic equation. This is often confused with logarithms not being defined for negative numbers. Here, $x=-1$ means that, on the LHS, we are calculating the logarithm of $(-1+4),$ a logarithm of a positive number, which is defined. No problems, $-1$ is a valid solution.