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

Can anybody please explain me .

Koolman
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  • The string "$100$" contains three digits. The number $T_{100}$ is the string "$100$" repeated a hundred times, so the total number of digits is (the number of digits in one string) times (the number of times the string is repeated), this gives $3 * 100 = 300$. Did you not understand how they got the number of digits, or why they are taking the number of digits? – Sarvesh Ravichandran Iyer Mar 29 '17 at 10:29
  • Hi. Please make questions stand on their own with text and typeset mathematics and not images of text or formula. If you already have over 1000 reputation you should know this. Voting to close. – mathreadler Apr 14 '17 at 05:19

1 Answers1

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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 $299$

Peter
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