Start with the linear approximation formula,

- $L(x) = f(a) + (x-a)f'(a).$

- $f(a) = \ln(1) = 0.$

- $f'(x) = 1/x,$ so that $f'(a) = 1/1 = 1.$

$L(x)=f(a) + (x - a)f'(a)$

$=0 + (x - 1)(1)$

$=\color{blue}{x - 1}.$

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