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If log 2 = 0.30103, then the number of digits in 5^20 ?
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If log 2 = 0.30103, then the number of digits in 5^20 ?
Solution:


Step 1: Finding the value of log(5^20)


We know that log(ab) = log(a) + log(b)

Therefore, log(5^20) = 20log(5)

Now, we need to find the value of log(5).

Step 2: Finding the value of log(5)


We can use the fact that log(2) = 0.30103 to find the value of log(5).

We know that 2 and 5 are both powers of 10, and that log(10) = 1. Therefore, we can write:

log(2) + log(5) = log(10)

0.30103 + log(5) = 1

log(5) = 0.69897

Step 3: Finding the number of digits in 5^20


Now that we know the value of log(5), we can go back to our original equation:

log(5^20) = 20log(5) = 20 x 0.69897 = 13.9794

This tells us that 5^20 is a number with a logarithm of 13.9794.

We know that the number of digits in a number is equal to its logarithm plus one, rounded down to the nearest integer.

Therefore, the number of digits in 5^20 is:

floor(13.9794 + 1) = floor(14.9794) = 14

Therefore, 5^20 has 14 digits.
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If log 2 = 0.30103, then the number of digits in 5^20 ?
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If log 2 = 0.30103, then the number of digits in 5^20 ? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If log 2 = 0.30103, then the number of digits in 5^20 ? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log 2 = 0.30103, then the number of digits in 5^20 ?.
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