First slide

Types of real valued functions XI

Question

Given that log (2)=0.3010..., the number of digits in the number 2000²⁰⁰⁰ is

Moderate

A

6601
B

6602
C

6603
D

6604

Solution

$Let x = 2000^{2000}$
$\begin{matrix} \log x = 2000 \log_{10} (2000) \\ = 2000 (\log_{10} 2 + 3) \\ = 2000 (3 .3010) = 6602 \end{matrix}$
Therefore, the number of digits is 6603.

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