We use the point slope formula
Since a = 1 {\displaystyle a=1} we obtain f ( a ) = ln ( 1 ) = 0 {\displaystyle f(a)=\ln(1)=0} , while f ′ ( x ) = 1 x {\displaystyle f'(x)={\frac {1}{x}}} implies f ′ ( a ) = 1 {\displaystyle f'(a)=1} . Hence
y − 0 x − 1 = 1. {\displaystyle \displaystyle {\frac {y-0}{x-1}}=1.}
Solving gives
y = x − 1 {\displaystyle \displaystyle y=x-1}
Thus, the approximation we seek is given by
y = 1.25 − 1 = 0.25 {\displaystyle \displaystyle y=1.25-1=0.25} .
we obtain 
, while 
implies 
. Hence
.
