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)
logab = 1/logba
logbn = logen/logeb
log10n = logen/loge10 = logen *(0.43429448..)

Tool to find logarithm value of a number

Solved problems:
Question 1: What is the value of STEP [ log25 ]?
log25 = log105 / log102
         = 0.6989/0.3010 { 2 < val < 3 }
STEP[log25 ] = 2

Question 2: Which is the bigger one 2^51 or 5^31 ?
 Solution: Apply Log10 both sides
                Log10(2^51) , Log10(5^31)
                51*Log102  , 31*Log105
                51*(0.3010) , 31*0.6989
                15.3 , 21.7  (Approximately)
so 5^31 is the bigger one.

Exercise problems:

  1. What is the value of 1/Log26 + 1/Log36 + log61
  2. What is the value of Log26
  3. Which is the bigger one 5^81 or 8^40 ?
  4. Which is smaller 1/(5^81) or 1/(125^3) ?
  5. What is the value of Log160006 
  6. What is the value of Log 1 
  7. What is the value of Log( -10 )
  8. Loge6 v/s Log106 which is bigger one

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