PPT: Logarithms | Physics for JEE Main & Advanced PDF Download

 Page 1


LOGARITHMS 
 
Page 2


LOGARITHMS 
 
INDICES 
? Any expression written as a
n
 is defined as the 
variable a raised to the power of the number n 
 
? n is called a power, an index or an exponent of a 
 
? Example - where n is a positive whole number,  
  a
1
 = a 
  a
2
 = a ? a  
  a
3
 = a ? a ? a  
  a
n
 = a ? a ? a ? a……n times  
 
 
Page 3


LOGARITHMS 
 
INDICES 
? Any expression written as a
n
 is defined as the 
variable a raised to the power of the number n 
 
? n is called a power, an index or an exponent of a 
 
? Example - where n is a positive whole number,  
  a
1
 = a 
  a
2
 = a ? a  
  a
3
 = a ? a ? a  
  a
n
 = a ? a ? a ? a……n times  
 
 
INDICES SATISFY THE FOLLOWING RULES  
? a
n
 = a ? a ? a ? a……n times 
 e.g. 2
3
 = 2 ? 2 ? 2  = 8 
 
?Negative powers….. 
 
 a
-n  
= 
 
  e.g. a
-2
  =  
 
 e.g. where a = 2 
 2
-1 
=    or   2
-2  
=  
n
a
1
2
1
a
2
1
4
1
2 2
1
?
?
Page 4


LOGARITHMS 
 
INDICES 
? Any expression written as a
n
 is defined as the 
variable a raised to the power of the number n 
 
? n is called a power, an index or an exponent of a 
 
? Example - where n is a positive whole number,  
  a
1
 = a 
  a
2
 = a ? a  
  a
3
 = a ? a ? a  
  a
n
 = a ? a ? a ? a……n times  
 
 
INDICES SATISFY THE FOLLOWING RULES  
? a
n
 = a ? a ? a ? a……n times 
 e.g. 2
3
 = 2 ? 2 ? 2  = 8 
 
?Negative powers….. 
 
 a
-n  
= 
 
  e.g. a
-2
  =  
 
 e.g. where a = 2 
 2
-1 
=    or   2
-2  
=  
n
a
1
2
1
a
2
1
4
1
2 2
1
?
?
? A Zero power 
  a
0
 = 1        
  e.g. 8
0
 = 1 
 
? A Fractional power 
 
 
  
e.g. 
 
    
n
a a
n
?
1
3 9 9 9
2
2
1
? ? ?
2 8 8
3
3
1
? ?
Page 5


LOGARITHMS 
 
INDICES 
? Any expression written as a
n
 is defined as the 
variable a raised to the power of the number n 
 
? n is called a power, an index or an exponent of a 
 
? Example - where n is a positive whole number,  
  a
1
 = a 
  a
2
 = a ? a  
  a
3
 = a ? a ? a  
  a
n
 = a ? a ? a ? a……n times  
 
 
INDICES SATISFY THE FOLLOWING RULES  
? a
n
 = a ? a ? a ? a……n times 
 e.g. 2
3
 = 2 ? 2 ? 2  = 8 
 
?Negative powers….. 
 
 a
-n  
= 
 
  e.g. a
-2
  =  
 
 e.g. where a = 2 
 2
-1 
=    or   2
-2  
=  
n
a
1
2
1
a
2
1
4
1
2 2
1
?
?
? A Zero power 
  a
0
 = 1        
  e.g. 8
0
 = 1 
 
? A Fractional power 
 
 
  
e.g. 
 
    
n
a a
n
?
1
3 9 9 9
2
2
1
? ? ?
2 8 8
3
3
1
? ?
ALL INDICES SATISFY THE 
FOLLOWING RULES IN MATHEMATICAL 
APPLICATIONS 
 
Rule 1  a
m
. a
n
 = a
m+n 
       e.g.   2
2
 . 2
3
 = 2
5
 = 32 
      e.g.   5
1
 . 5
1
 = 5
2
 = 25 
      e.g.   5
1
 . 5
0
 = 5
1
 = 5 
 
Rule 2  
 
 
        
n m
n
m
a
a
a
?
?
8 2 2
2
2
2
2 2 2
2
2
1
3 0 3
0
3
1 2 3
2
3
? ? ?
? ? ?
?
?
. .
. .
g e
g e