# Quantitative Reasoning : Logarithms

## Question

How many digits will the number 3

^{200} have if the value of log

_{10}3 = 0.4771?

- 95
- 94
- 96
- 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, log

_{10}3, the value of log

_{10}3 = 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 log

_{10}30 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 3

^{200}.

If we take log we get log

_{10}3

^{200} = 200(log

_{10}3) = 200 (0.4771) = 95.42.

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

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