this doubt is with reference to ...chemistry(part 1)-page no 269-appendix-illustration 2....

please explain me how we arrive the following step..

log x = 0.13485 - 1.0492 - 1.3711 = -3.71455

( i dont know how we get the final value as -3.7145 ....i get as -2.28545 on simplification)

You are right. On simplification, we get -(2.28545).

But, as we know, mantissa (decimal part) can never be negative.

So, -2.28545 can be written as:

-(2 + 0.28545) = -2 - 0.28545 (+ 1 - 1) = - 2 - 1 + 1 - 0.29545 = 3.7145 ( 3 means "3 bar" - only 3 is negative which is, hence, required as the characteristics can be negative).

Hope you understood.