Start with the linear approximation formula,

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,


Substituting all of this in the formula gives

$L(x)=f(a) + (x - a)f'(a)$
       $=0 + (x - 1)(1)$
       $=\color{blue}{x - 1}.$

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