Characterstic of log

Question

I could not understand how they got $T_{100}$ as 300 .

Can anybody please explain me .

Answer 1

Since the string consisting of $100$ times "$100$" has $300$ (decimal) digits, we have $$10^{299}< \underbrace{100100\cdots 100100}_{100\ times\ "100"}<10^{300}$$ hence the integer part of the decimal logarithm is $299$