Start with the linear approximation formula,
$L(x) = f(a) + (x-a)f'(a).$
We need to substitute for $\color{blue}{a}, \color{blue}{f(a)}$ and $\color{blue}{f'(a)}.$
We are told that $a = 1$ (that is the point near which we are approximating the logarithm). Thus,
and
$f'(x) = 1/x,$ so that $f'(a) = 1/1 = 1.$
Substituting all of this in the formula gives
$L(x)=f(a) + (x - a)f'(a)$
$=0 + (x - 1)(1)$
$=\color{blue}{x - 1}.$
Close this window to return to the on-line text.
Lost the on-line text window to which this window is attached? Press here.