Chapter 6 - Inverse Functions - 6.3 Logarithmic Functions - 6.3 Exercises - Page 426: 8

(a) $\frac{1}{2}$ (b) 3

(a) Use logarithmic property, $y logx=logx^{y}$ $e^{-ln2}=e^{ln2^{-1}}=e^{ln(\frac{1}{2})}$ Thus, $e^{-ln2}=\frac{1}{2}$ (b) Use logarithmic property, $y logx=logx^{y}$ $e^{ln(ln(e^{3}))}=ln(e^{3})$ $=3lne$ Since, $lne=1$ Hence, $e^{ln(ln(e^{3}))}=$ 3