LOGARITHMS - KEA | Home · 2012-02-18 · Common Logarithms: 1. Logarithm with base 10 is called...
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LOGARITHMS LOGARITHMS
Transcript of LOGARITHMS - KEA | Home · 2012-02-18 · Common Logarithms: 1. Logarithm with base 10 is called...
LOGARITHMSLOGARITHMS
If ‘a’ is a positive real number, other than one and then ‘x’ is called the than one and then x is called the “logarithm of ‘m’ to the base ‘a’ we
it write
RULES OF LOGARITHMS
Note:
Common Logarithms: Common Logarithms:
1. Logarithm with base 10 is called common logarithm.
2. The integral part of a logarithm is called its characteristic.
3. Antilogarithms: If y = log x , then x is called the antilogarithm of y to the called the antilogarithm of y to the base 10, we denote this by x= Antilog yx= Antilog y
11.
1)1 2)
3) 4)) )
S l ti Gi Solution: Given
U i Using
(Ans : 1 )
2.
1) 22 2) 1) 22 2)
3) 4) 3) 4)
Solution: Using
and by change of base rule we getand by change of base rule, we get
=
=
( Ans: 3)
3 If a b c are three 3. If a, b, c are three Consecutive integers Consecutive integers Then
1) 2)
3) 4)
Solution: Let
Where n is a positive integer
Let
(Ans : 1)
4. the number
of digits in is g
1)18 2) 3) 4) 3) 4)
l i Solution: Let
Since the characteristic is 19.
Thus, there are 20 digits in the integral
part part.
(Ans : 3)
5. the number of 5. the number of
zeroes between the decimal point
and the first significant figure in
i is
1)14 2) 3) 4) ) )
Solution: Let
Since the characteristic is thus the
required number of zeroes are
(Ans : 2 ) (Ans : 2 )
6. If
1) 2)
3) 4) 3) 4)
S l ti Solution:
let let
Canceling log and Squaring on both side,
we get
(Ans : 1 )
7 If then 7. If then
1)1 2)
3) 4)
S l tiSolution:
G.E.=G.E.
=
=
(Ans : 3 ) (Ans : 3 )
8. If
1) 2)
3) 4) 3) 4)
Solution:
G.E:
Now
(Ans : 3) (Ans : 3)
9.
1) 2) 1) 2) 3) 4)
Solution: G.E.
(Ans : 3 )( )
10 If 10. If
1) 2) 1) 2)
3) 4)
Solution:
We have
Using and
change of base rule we get change of base rule, we get
=
(Ans : 3)
11 If11. If
1) 2) 3) 4) 3) 4)
Solution: Here
G.E.
(Ans : 1)
12. If
1) 2)
3) 4) 3) 4)
Solution:
Let
(Ans: 4)
13. If
1) 2) 1) 2)
3) 4)
Solution: Put then
(Ans: 4)
14.
If If
1) 2) 3) 4)
Solution:
(Ans: 2)
15. 15.
1) 2) ) ) 3) 4)
Solution:
Let
. (Ans: 2)
16 = 16. =
1) 2) 1) 2)
3) 4)
Solution: LetSolution: Let
==
=
=
(Ans: 2) (Ans: 2)
17. =
1) 2) 1) 2) 3) 4)
Solution: using
Let
G.E.=
(Ans: 4)
1818.
1) 2)
3) 4)
Solution:
Canceling log
(Ans : 1)
19.19.
1) 2)
3) 4) 3) 4)
Solution: G E G.E.
= =
=
(Ans : 2)
20.
=
1) 2) 1) 2)
) ) 3) 4)
Solution:
(Ans : 3)
21.
1) 2) 3) 4) 3) 4)
Solution:
LetLet
l l b h id dCancel log on both side and cross multiplying we getmultiplying ,we get
(A 1) (Ans: 1)
22.
) ) 1) 2)
3) 4) 3) 4)
Solution:
Let
(Ans: 3) (Ans: 3)
23.
1) 2) 1 1) 2) 1 3) 4)
Solution:Solution:
G.E. =
=
=
(Ans: 2)
24.
1) 2) 1) 2) 3) 4) ) )
Solution:
G.E.=
=
=
( ) (Ans : 1)
