IPMAT Indore 2024 (MCQ) - The numbers 2^2024 and 5^2024 are expanded and their digits are written out consecutively on one page. The total number of digits written on the page is | PYQs + Solutions | AfterBoards
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IPMAT Indore 2024

Modern Math
>
Logarithms

Medium

The numbers 220242^{2024} and 520245^{2024} are expanded and their digits are written out consecutively on one page. The total number of digits written on the page is

Correct Option: 2
Even without knowing the values of the log, you can still solve it (take base as 10):
log⁡22024+log⁡52024\log 2^{2024} + \log 5^{2024} \newline =2024log⁡2+2024log⁡5= 2024 \log 2 + 2024 \log 5 \newline =2024(log⁡2+log⁡5)= 2024 (\log 2 + \log 5) \newline =2024[log⁡(2×5)]= 2024 [\log (2 \times 5)] \newline =2024(log⁡10)= 2024 (\log 10) \newline =2024×1= 2024 \times 1 \newline The number of digits is always one more than the resultant value, i.e. 20252025 digits, and no other option is close to this.

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