### Logarithm problem, log question, Answers. Math Prep. Ascent MBA TANCET, XAT, CAT, PGSEM Correspondence course, Classes

 Home TANCET Classes GMAT Coaching Online GMAT Course CAT Classes TANCET Study Material
 TANCET '18 Classroom Program Weekend and weekday classes for TANCET MBA @ Chennai. At Nungambakkam and Velachery. Other Courses TANCET Correspondence Course CAT Classes & Courses GMAT Classes Chennai Online GMAT Course GRE Classes Chennai CBSE Math Online Tuition SAT Classes Other Links Ascent TANCET Toppers Testimonials CAT, TANCET Questions Careers @ Ascent Contact Us +91 44 4500 8484 +91 96000 48484 ascent@ascenteducation.com Postal Address Facebook / Twitter / Blog / Videos
You are here: Home  »  CAT, XAT, TANCET Prep Questions »  Miscellaneous Topics »   Logarithm

# 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

Choice (3). 96 digits

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.

## CAT, XAT, TANCET Practice Questions and Answers : Listed Topicwise

 Number Theory Permutation Combination Probability Inequalities Geometry Mensuration Trigonometry Coordinate Geometry Percentages Profit Loss Ratio Proportion Mixtures Alligation Speed Time Distance Pipes Cisterns Interest Races Average, Mean AP, GP, HP Set Theory Clocks Calendars Algebra Function English Grammar General Awareness Data sufficiency TANCET Papers XAT Papers Add to del.icio.us Stumble It digg this