### Logarithm quantative aptitude question and answers

Logarithms have a wide range of applications in solving problems which are based not only on logarithms but also on the problems like finding the bigger number of 2^51 and 5^30. Logarithms also have many other applications which when used gives an immense sense of its usage.

What is a Logarithm?

A Logarithm is a quantity which represents the rise of it in terms of another number (base)

How it was derived, is there any formula to get logarithmic values?

Yes, there is a series called logarithmic series which will generate value of the logarithms

The main terms which one should be more familiar with before solving logarithmic problems are

Exponent: Power of a number.

Base: The number to reduce another number when log is applied.

Some Basic Logarithmic formula:

log ab = log a + log b

log a/b = log a - log b

log(a^b) = b*log(a)

log

log

log

Tool to find logarithm value of a number

*********************************************************************************

Solved problems:

Question 1: What is the value of STEP [ log

Solution:

log

= 0.6989/0.3010 { 2 < val < 3 }

STEP[log

Question 2: Which is the bigger one 2^51 or 5^31 ?

Solution: Apply Log10 both sides

Log10(2^51) , Log10(5^31)

51*Log

51*(0.3010) , 31*0.6989

15.3 , 21.7 (Approximately)

so 5^31 is the bigger one.

Exercise problems:

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Logarithms |

A Logarithm is a quantity which represents the rise of it in terms of another number (base)

How it was derived, is there any formula to get logarithmic values?

Yes, there is a series called logarithmic series which will generate value of the logarithms

The main terms which one should be more familiar with before solving logarithmic problems are

Exponent: Power of a number.

Base: The number to reduce another number when log is applied.

Some Basic Logarithmic formula:

log ab = log a + log b

log a/b = log a - log b

log(a^b) = b*log(a)

log

_{a}b = 1/log_{b}alog

_{b}n = log_{e}n/log_{e}blog

_{10}n = log_{e}n/log_{e}10 = log_{e}n *(0.43429448..)Tool to find logarithm value of a number

*********************************************************************************

Solved problems:

Question 1: What is the value of STEP [ log

_{2}5 ]?Solution:

log

_{2}5 = log_{10}5 / log_{10}2= 0.6989/0.3010 { 2 < val < 3 }

STEP[log

_{2}5 ] = 2Question 2: Which is the bigger one 2^51 or 5^31 ?

Solution: Apply Log10 both sides

Log10(2^51) , Log10(5^31)

51*Log

_{10}2 , 31*Log_{10}551*(0.3010) , 31*0.6989

15.3 , 21.7 (Approximately)

so 5^31 is the bigger one.

Exercise problems:

- What is the value of 1/Log
_{2}6 + 1/Log_{3}6 + log_{6}1 - What is the value of Log
_{2}6 - Which is the bigger one 5^81 or 8^40 ?
- Which is smaller 1/(5^81) or 1/(125^3) ?
- What is the value of Log
_{1}60006 - What is the value of Log 1
- What is the value of Log( -10 )
- Log
_{e}6 v/s Log_{10}6 which is bigger one

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