Question Set for mark 1:
Evaluate the following Logarithmic expressions:
Please note that when base is not mentioned, it is considered as Natural Logarithms.
13
log2 64
log10(0.001)
log32 ÷ log16
3(log94)
log2 (1/8)
log2+log(1/2)
log 9
Ans. 6
Ans . -3
Ans. 5/4
Ans. 2
Ans. -3
Ans. 0
Ans. -2
15
log5+log3
Ans. log15
1
3
5
7
9
11
2
4
6
8
10
12
14
log3(1/27)
log32-log16
27(log3 2)
49
log8 2
log5 625
If log =1,then x=?
Ans. -3
Ans. log2
Ans. 8
. 2
Ans. 1/3
Ans. 4
Ans. 2
Question Set for mark 3:
Simple Examples:
1
2
3
4
Find the value of log(9/14) - log(15/16) + log(35/24)
Prove that log(75/16) – 2log(5/9) + log(32/243) = log2
Ans. 0
Simplify : log
Ans. 0
5
Prove that
6
7
8
Simplify log 84 log 28 3'()*
Solve : 2 3 +
#
27 +
9.
Solve: log -log -log .. = 1
1
1
1
Prove that
+
+
= 2.
log 6 24 log12 24 log 8 24
9
10
+ log
+ log
1 ] +log[x - √
Prove that log[x +√
Prove that: log /
!
"
+ log
!
"
!
#0
+ log 0 1 + log 2 3 = 24
1 ]=0
Ans. 0
Ans. 27
Ans. 512
11
Prove that
+
'()
=1
'()*
12
13
Prove that:log 2 1 + log1 3 + log3 4 = log 2 4
If log5 3 -log 25 = log then find the value of “ x”.
14
If
15
If log
789 +7892
789:
Ans. 5
Ans. 3√3
= log27, Then find the value of “ x”.
= 2 and log 2 1 =2 ,then find the value of “ y”.
Ans. 16
Question Set for mark 4:
Examples based on Theorems/Rules:
1
Prove that
2
Prove that
3
If log
A
'();
" '()
!
'()<= >
+
<
'()=; >
!
+
" '()
!
=
'();< >
# 1.
= 2 log > 5?@.
= (log 5 + log ?) , prove that a = b.
4
Prove that : log B + log
5
Prove that
6
Prove that
7
Prove that
8
Solve the following equation: log-2 " 1. + log-3
9
 x+ y 1
2
2
If log 
 = (log x + log y ) , then prove that x + y = 7 xy
 3  2
10
If
B + log
*
B + log
C
B = 4 log B
 a−b 
 b−c 
c−a 
log x 
 + log x 
 + log x 
=0.
 b−c 
c−a
 a −b 
log
q
'()D /0A
'()I JA'()I : .
'()I J
p 2 ⋅ log r q 2 ⋅ log
+
'()E 02A
p
+
r 2 = 64
'()F 2/A
=1
1. = 0.
= log K Then find the value of “x”
Ans. x =
Ans.x=25