Given that `log(2)=0. 3010 ,` the number of digits in the number `2000^(2000)` is 6601 (b) 6602 (c) 6603 (d) 6604

Explanation

To find the number of digits in the number \( 2000^{2000} \), we can follow these steps:

### Step 1: Express the number in terms of logarithms
Let \( y = 2000^{2000} \). We will use logarithms to find the number of digits in \( y \).

### Step 2: Use the logarithmic identity
We know that the number of digits \( d \) in a number \( n \) can be found using the formula:
\[
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