Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 3

True.

Yes. When we defined a logarithmic function, we defined it as the inverse function of an exponential function $f(x)=a^{x}$, which has the range $(0,+\infty)$. The range of f is the domain of $\log_{a}x$, so logarithms are defined for positive numbers only.