Science:Math Exam Resources/Courses/MATH104/December 2010/Question 01 (n)/Solution 1

We use the linear approximation of $\ln (x)$ at $x=1$ to estimate $\ln (0.8)$. (Approximating at x = 1 is a logical choice, as 1 is close to 0.8, and we know that $\ln (1)=0$.)

We know $\frac{d}{dx}\ln (x)=\frac{1}{x}$, which is equal to 1 when $x=1$. Substituting this into the linear approximation formula, we get,

$\ln (0.8)\approx \ln (1)+1(0.8-1)=0-0.2=-0.2$