Quantitative Reasoning : Logarithms

Question

How many digits will the number 3²⁰⁰  have if the value of log₁₀3 = 0.4771?

1. 95
2. 94
3. 96
4. 91
   
   

Correct Answer

Choice (3). 96 digits

Explanatory Answers

The logarithm of any number has two components. The characteristic and the mantissa.

Take for example, log₁₀3, the value of log₁₀3 = 0.4771.
Here, the 0 in the integral part is known as the characteristic and the value .4771 is known as the mantissa.

The value of log₁₀30 is 1.4771.
Notice that the value of mantissa remained the same while that of the characteristic changed from 0 to 1.

Given the log of a number, we will be able to find out the number of digits that the original number had by knowing the value of the characteristic.

If the characteristic is '0', then the number is a single digit number
If the characteristic is '1', then the number is a two-digit number
If the characteristic is '5', then the number is a six-digit number

In the given problem, we need to find the number of digits of 3²⁰⁰.

If we take log we get log₁₀3²⁰⁰ = 200(log₁₀3) = 200 (0.4771) = 95.42.

Here, the characteristic is 95. Therefore, the number will have 96 digits.

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