14. Suppose that $(21.4)^{e}=(0.00214)^{b}=100$. Find the value of $\frac{1}{a}-\frac{1}{b}$.
14. Answer: 2
We have $a=\frac{2}{\log _{10} 21.4}$ and $b=\frac{2}{\left(\log _{10} 21.4\right)-4}$. Hence direct computation yields $\frac{1}{a}-\frac{1}{b}=2$.