Chapter 2.4, Problem 13P

Fun with logarithms.

(a) Simplify the expression $e^{a\ln b}$. (That is, write it in a way that doesn’t involve logarithms.)

(b) Assuming that $b\ll a$, prove that $\ln \left(a+b\right)\approx \left(\ln a\right)+\left(b\text{/}a\right)$. (Hint: Factor out the a from the argument of the logarithm, so that you can apply the approximation of part (d) of the previous problem.)