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Logarithm - Quant/Math - CAT 2009
Question 4 the day:
July 21, 2003
The question for the day is from the topic of Logarithm.
- How many digits will the number 3^200 have if the value of log 3 = 0.4771?
| (1) |
95 |
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(2) |
94 |
| (3) |
96 |
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(4) |
None of these |
Correct Answer - (3)
Solution:
In any logarithm, the value has two components. The characteristic and the mantissa.
Take for example, log 3, the value of log 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 30 would be equal to 1.4771. Notice that the value of mantissa remained the same while that of the characteristic changed from 0 to 1.
For any given logarithmic value, 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 case of 3200, if we take log we get log 3200 = 200 log 3
= 200 (0.4771) = 95.42.
Here, the characteristic is 95. Therefore, the number will have 96 digits.
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