Find the linear approximation of f(x)=lnx at x=1

L(x)= ?

I can't get this half of the question

The whole question is:
Find the linear approximation of f(x)=lnx at x=1 and use it to estimate ln1.21.

I know the estimation part, but I think I did something wrong with the first part

The linear approximation L(x) of f(x) at x=a is given by:
L(x) = f(a) + f'(a)(x - a)

In this case, f(x) is lnx and a is 1, so we have:
f(x) = lnx
f(a) = ln(a) = ln(1) = 0
f'(x) = 1/x
f'(a) = f'(1) = 1/1 = 1
L(x) = f(a) + f'(a)(x-a)
L(x) = 0 + 1(x - 1)
L(x) = x - 1

So, the linear approximation is L(x) = x - 1.

To approximate ln(1.21), plug in 1.21 for x:
L(x) = x - 1
L(1.21) = 1.21 - 1
L(1.21) = 0.21

So the approximation of ln(1.21) is 0.21, which is reasonably close to the actual value of approximately 0.19.

Hope that helps :)