Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 1

False.

No, this is often confused with the argument of a logarithmic function needing to be positive. For example, the equation $ \log_{2}(x+2)=0$ has a negative solution, $x=-1$ (because $2^{0}=1$, and $\log_{2}1=0)$ The negative solution is such that the argument of the logarithm is still positive.