Chapter 6 - Inverse Functions - 6.3 Logarithmic Functions - 6.3 Exercises - Page 426: 4

(a) $-3$ (b) $-2$

(a) Use logarithmic base formulas $\log_{b}x=\frac{log x}{log b}$ and $\log b^{x}=x log b$ $log_{5}\frac{1}{125}=\frac{log\frac{1}{125}}{log5}=-3$ (b) $ln(\frac{1}{e^{2}})=log_{e}(\frac{1}{e^{2}})$ Hence, $ln(\frac{1}{e^{2}})=-2$