How to find M in tangent line error bound (taylor polynomials)

How to solve for "M" in error bound calculations?

Just need help on solving for M and then i'm Ok (i think)

heres the prob:

f(x) = Ln(x), b=1, and i need to use tang line error bound to find interval so that error is at most .01 on J.

So... heres what i set up:

f(x) = / Ln(x) - [x-1] \ <= M/2 /x-1\ <= .01

So i need to find "M" right?

So.. M/2 /x-1\ <= .01

And thats where i get stuck.. can't seem to solve for M

Correct me if wrong, but if i could solve for M then i could find a suitable interval, right??

Please help someone -thanks alot!:)

PS:

/ \ (absolute value)

<= (greater than or equal to)