LOGARITHMS : Subhash LOGARITHMS
Definition : Definition ax = N
log a N = x
102 = 100
log 10 100 = 2
34 = 81
log 381= 4
Domain : Domain log a N = x
N : Positive real number
Base : Positive real number other than 1
X : Any real number
Examples : Examples log 5 125 = ?
5x = 125
x = 3
log 3 9= ?
3x = 9
x = 2
log 1 8= ?
1x = 8
Base cannot be 1
Rules : Rules Log a a= 1 (a1 = a)
Log a 1= 0 (a0 = 1)
Log (1/m) = - log m
Log (m*n) = log m + log n
Log (m/n) = log m – log n
Log b a = 1/ Log a b
Log am= m Log a
Rules : Rules Log a m/n = Log a m - Log a n
Log a m = x ? ax = m
Log a n= y? ay = n
m/n = ax / ay = ax-y
Log a m/n = x – y Memorize All The Rules
Simplify : Simplify Log (x+2) + Log (x-2 ) = log 32
? Log [( x+2)*(x-2)] = log 32
? x2 - 4 = 32
? x = +6 or -6
x = +6
Example : Example If a is a positive number less than 1, the Log 5 a is
Greater than 1
Positive number less than 1
Negative
Not defined
5x is less than 1
x must be Negative
Slide 9 : How many trailing zeros are there at the end of N! The highest power of 3 in N! is 8
The highest power of 3 in N! is 14 Can be answered using A alone, but not B
Can be answered using B alone, but not A
Can be answered using both A and B together
Can not be answered even by using A and B together 1, 2,3,4,5,6,7,8,9,10,…,12,…15,…18,…21…24,…27…30,…33 A: N = 18,19 or 20 B: N = 30,31,32 5,10,15 5,10,15,20,25,30
Thank You : Thank You
Types of Logarithms : Types of Logarithms Natural Logarithms
Base = e ( Approx 2.71828183 )
Common Logarithms
Base = 10
Common Logarithms : Common Logarithms Log 10 40= ?
10x = 40
1. _ _ _
Characteristic
(Number of digits - 1)
Mantissa
Decimal part