I am unable to solve the following question as i don't understand what the relationship is between significant figures and Logarithms.
Q-If $\log_{10}(7)= 0.8451$ then the position of the first significant figure of $7^{-20}$.
The answer is the position of the first significant figure is 17th.
My book solves it in the following method-
$$\log_{10}(x)=-20\log_{10}(7)$$
$$=-16.9020 =-17+1-0.9020 = \bar17 .0980$$
so the position is 17.
I fail to understand how and why this has happened please explain this solution to me and the relationship between significant figures and Logarithms...