1.
Log 6 + log 5 is expressed as
(a) Log 11
(b) Log 30
(c) Log 5/6
(d) None of these
2.
Log28 is equal to
(a) 2
(b) 8
(c) 3
(d) None of these
3.
Log 32/4 is equal to
(a) log 32 / log 4
(b) log 32 - log 4
(c) 8
(d) None of these
4.
Log (1x2x3) is equal to
(a) Log1 + log2 + log3
(b) Log3
(c) Log2
(d) None of these
5.
The value of log 0.0001 to the base 0.1 is.
(a) -4
(b) 4
(c) 1/4
(d) None of these
6.
If 2 log x = 4 log3, then x is equal to (a) 3
(b) 9
(c) 2
(d) None of these
7.
√
64 is equal to
(a) 12
(b) 6
(c) 1
(d) None of these
8.
If log a√ = 1/6, find the value of 'a'.
(a) 8
(b) 4
(c) 3
(d) 1
9.
√
1728 is equal to
(a) 2√
(b) 2
(c) 6
(d) None of these
10.
The logarithm of 21952 to the base of 2√ and 19683 to the base of 3√ are
(a) Equal
(b) Not equal
(c) Have a difference of 2269.
(d) None
11.
log (3 - 2) is equal to
(a) 4
(b) 3
(c) 0
(d) 
12.
The value of (log8128) x log6
(a) -7
is
(b) 7
(c) 1/7
(d) -2/7
13.
Log (1/81) to the base 9 is equal to
(a) 2
(b) 1/2
(c) -2
(d) None of these
14.
The
√
324
(a) 2
(b) 3
(c) 4
(d) 1
15.
Find the base in logarithm of 32 is 10/3.
(a) 5/3
(b) 20/9
(c) √
(d) 4
16.
Log( 12 + 22 + 32) is equal to
(a) log 12 + log 22 + log 32
(b) log 2 + log 7
(c) log 2 - log 7
(d) None of these
17.
If
, then the value of x is
(a) 5
(b) 0.25
(c) 0.5
(d) 25
18.
Evaluate log(logx2) - log(Iogx).
(a) 2
(b) log 2
(c) log x
(d) log √
19.
The value of
(a) -1
(b) 1
(c) loga b
(d) loga (ab)
is
20.
If Log e m + log e n = Log e (m + n), then find m as a simple function of n.
(a) 1/n
(b) n2
(c) n2 x (n - 1)
(d) n / (n -1)
21.
If log10y = 1 + 2log10x - log10z then value of
is
(a) 10
(b)
(c) 100
(d)
22.
If log(
)
(log a + log b), then
(a) a = b/2
(b) a = b
(c) a = b2
(d) a2 = b
23.
Given log 2 = 0.03010 and log3 = 0.4771 the value of log 6 is
(a) 0.9030
(b) 0.9542
(c) 0.7781
(d) None of these
24.
The value of log8 25 given log 2 = 0.3010 and log 5 = 0.6989 is (a) 1
(b) 2
(c) 1.5482
(d) None of these
25.
If 3 + log10x = 2log10y, then value of x in terms of y will be
(a) (2/3)y
(b) Y2/10
(c) 10y
(d) Y2/1000
26.
Value of log (1+2+3+ ........ +n) is equal to (a) log 1 + log 2 + ....... + log n
(b) log n + log (n+1) - log 2
(c) 0
(d) 1
27.
If log (x + y) = log (
), log x - log y =
(a) log 2
(b) log 3
(c) log 5
(d) log 6
28.
( )
(
)
=
(a) 3
(b) 3/2
(c) 2
(d) 1
29.
log10 25 - 2 log103 + log1018 equals -
(a) 18
(b) 1
(c) log10 3
(d) None of these
30.
log
- 2 log + log
reduces to
(a) 2 log 2
(b) 5 log 2
(c) log 2
(d) 4 log 2
31.
Value of 16 log
+ 12 log
+ 7 log
+ log 2 is
(a) 0
(b) 1
(c) 2
(d) -1
32.
Solve log(
) + log 2 = log 5
(a) 0
(b) 3 or
(c) or 2
(d) 1
33.
If log2[log3(log2 x)] = 1, then x equals
(a) 128
(b) 256
(c) 512
(d) None of these
34.
7log ( ) + 5 log( ) + 3log ( ) is equal to
(a) 0
(b) 1
(c) log 2
(d) log 3
35.
If loga(ab) = x, then logb(ab) is
(a)
(b)
(c)
(d)
36.
The value of log2[log2{log2(log3(273))}] is
(a) 1
(b) 0
(c) 2
(d) 3
37.
If log2x + log4 x + log16x =
, then x equals
(a) 8
(b) 4
(c) 2
(d) 16
38.
If loge 2.logb 625 = log1016.loge10, then b =
(a) 4
(b) 5
(c) 1
(d) e
39.
The value of
√
√
(a) log 2
(b) 1
(c) 0
(d) None of those
40.
If logab = logbc = logca, then
(a) a > b > c
is
(b) a < b < c
(c) a = b = c
(d) a < b < c
41.
log(√
√
) Simplifies to
(a) 3/2 log a + 2/3 log b
(b) 6(log a + log b)
(c) 2/3 log a + 3/2 log b
(d) None of the above
42. log3 √
√
simplifies to
(a) -log 3
(b) 2 log 3
(c) log a
(d) 4 log 2
43.
The simplified value of log2. log2, log216 is
(a) 0
(b) 2
(c) 1
(d) None of these
44.
If log2 x + log4 x + log16 x = 21/4, these x is equal to
(a) 8
(b) 4
(c) 16
(d) None of these
45.
Given that log102 = x and log10 3 = y, the value of log10 60 is expressed as
(a) x - y + 1
(b) x + y + 1
(c) x - y - 1
(d) None of these
46.
log[
{
} ]
can be written as
(a) Log x2
(b) Log x
(c) Log 1/x
(d) None of these
47.
is
(a) 0
(b) 1
(c) 2
(d) -1
48.
is(a) 0
(b) 1
(c) 3
(d) -1
49.
logb(a) . logc (b) loga(c) is equal to
(a) 0
(b) 1
(c) -1
(d) None
50.
The value of
is
(a) 0
(b) 1
(c) -1
(d) None
51.
The value of
(a) 0
(b) 1
is
(c) -1
(d) None
52.
The value of log
+ log
+ log
+ log
+ log
is
(a) 0
(b) 1
(c) -1
(d) None
53.
The value of log
(a) 0
(b) 1
(c) -1
(d) None
54.
log(a - 9) + log a = 1, the value of 'a' is (a) 0
(b) 10
(c) -1
(d) None
55.
If
the value of abc is
(a) 0
(b) 1
(c) -1
(d) None
56.
If
log c the value of ay+z . bz+x . cx+y is given by
(a) 0
(b) 1
(c) -1
(d) None
57.
If log a = log b = log c the value of a4b3c-2 is
(a) 0
(b) 1
(c) -1
(d) None
58.
If log a = log b = log c the value of a4 - bc is
(a) 0
(b) 1
(c) -1
(d) None
59.
If log 2 +
log a + log b = log(a + b), then -
(a) a = b
(b) a = - b
(c) a = 2, b = 0
(d) a = 10, b = 1
60.
If
then the value of z is-
(a) abc
(b) a+b+c
(c) a(b+c)
(d) (a+b)c
61.
Find the value of Im + mn + nl - lmn, if l = 1 + logabc, m = 1 logbca, n = 1 + logcab
(a) 0
(b) 1
(c) -1
(d) 3
62.
If a = b2 = c3 = d4 then the value of loga(abcd)i
(a)
(b)
(c) 1 + 2 + 3 + 4
(d) None
63.
The sum of the series
loga b + loga2 b2 + loga3 b3 + ... logan bn is given by
(a) loga bn
(b) logan bn
(c) n logan bn
(d) None
64.
The value of the following expression
is given by
(a) t
(b) abcdt
(c) (a+b+c+d+t)
(d) None
65.
If a2 + b2 = 7ab, then the value of
is
(a) 0
(b) 1
(c) -1
(d) 7
66.
If a3 - b3 = 0 then the value of log a + b - (log a + log b + log 3) is
(a) 0
(b) 1
(c) -1
(d) None of the above
67.
If x = loga bc y = logb ca z = logc ab then the value of xyz - x - y - z is
(a) 0
(b) 1
(c) -1
(d) 2
68.
On solving the equation log t + log(t - 3) = 1 we get the value of t as (base 10)
(a) 5
(b) 2
(c) 3
(d) 0
69.
On solving the equation
⌋ = 1 we get the value of t as -
⌊
(a) 8
(b) 18
(c) 81
(d) 6,561
70.
On solving the equation
[
] = 2 we get the value of t as
(a) 5/2
(b) 25/4
(c) 625/16
(d) None
71.
If logabc = x, logbca = y, logcab = z,
(a) 0
(b) 3
(c) x+y+z
is equal to
(d) 1
72.
If a = log 24 12, b = log 36 24, and c = log 48 36, then 1 + abc
(a) 1
(b) 2
(c) 2bc
(d) Abc
73.
If
, xq+ryr+pzp+q equals
(a) xpyqzx
(b) 1
(c) 0
(d) xyz
74.
If a2 + b2 = c2,
is
(a) 2
(b) 1
(c) log abc
(d) 0
75.
If
, then x2y2z2 equals -
(a) 2
(b) -1
(c) 4
(d) 1
76.
If x2 + y2 = 7xy then 2 log (x+y) equals
(a) 2(log 3 + log x + log y)
(b) 2 log 3 + log x + log y
(c) 2(log x + log y) + log 3
(d) None of these.
77.
The equivalent form of the equation log (x-2) + log (x+3) = 0 is
(a) x2 + x - 5 = 0
(b) x2 - x - 5 = 0
(c) x2 + x - 7 = 0
(d) None of the above
78.
If log2(32x-2 + 7) = 2 + Iog2(3x-1 + 1) then x equals
(a) 0
(b) 1
(c) 2
(d) 1 or 2
79.
Iog5(
) + Iog 5(
) + log 5 (
) + .......... + log 5 (
(a) 5
(b) 4
(c) 3
(d) 2
80.
If log(x - y) - log 5 - log x - log y = 0,
(a) 25
equals
)
(b) 26
(c) 27
(d) 28
81.
The value of
is
(a) log xyz
(b) 1
(c) 2
(d) None of these
82.
Value of log3 2log4 3log4 4....log15 14log16 15 is
(a) 1/3
(b) 1/2
(c) 1/5
(d) 1/4
83.
If a3 + b3 = 0, then the value of log(a + b) - (log a + log b + log 3) is equal to
(a) 0
(b) 1
(c) -1
(d) 3
84.
If
√
is equal to
(a) 1
(b)
(c)
(d) 0
85.
If x = loga bc, y = logb ca, z = logc ab, then
(a) xyz = x + y + z + 2
(b) xyz = x + y + z + 1
(c) x + y + z = 1
(d) xyz = 1
86.
If
, then yz in terms of x is
(a) x
(b) x2
(c) x3
(d) x4
87.
The difference between the logarithms of sum of squares of two positive numbers A and B and
the sum of the logarithms of the individual numbers is a constant C. If A=B, then C is
(a) 2
(b) 1.3031
(c) log 2
(d) exp(2)
88.
If
= log(m + n), then
(a) m + n = 1
(b)
(c) m - n = 1
(d) m2 . n2 = 1
89.
If log30 3 = a, log30 5 = b, then log30 8 =
(a) 3(1 - a - b)
(b) (a - b + 1)
(c) (1 - a - b)
(d) 1(a - b + 1)
90.
If
, then a, b, c are in -
(a) G.P
(b) A.P
(c) H.P
(d) None of these
91.
If x = 1983, then value of expression
is -
(a) 0
(b) 1
(c) 2
(d) 3
92.
log(x - y) - log 5 - log x - log y = 0, then
(a) 25
(b) 26
(c) 27
(d) 28
=
93.
If a2 + b2 = 0, and a + b  0 then the value of log(a + b) is (a) log a + log b + log 2
(b) (log a + log b + log 2)
(c) log a + log b
(d) None of these
94.
If logx+2(x3 - 3x2 - 6x + 8) = 3, then x =
(a) 2
(b) -2
(c) 1/2
(d) None of these
95.
If log
(log x + log y), then
(a) 20
(b) 23
(c) 22
(d) 21
96.
If log(2a - 3b) = log a -log b, then a =
(a) 3b2 / (2b - 1)
(b) 3b / (2b - 1)
(c) B2 / (2b + 1)
(d) 3b2 (2b + 1)
=
97.
2log(a + b) + log(a - b) - log(a2 - b2) = log x, then x =
(a) (a + b)
(b) a - b
(c) a2 - b2
(d) None of these.
98.
The value of logb a . logcb . logac is
(a) 0
(b) log abc
(c) 1
(d) 10
99.
If
, then 3(x+y) . 5(y+z) . 7(z+x) =
(a) 2
(b) 10
(c) 1
(d) 0
100.
{
(a) log ab
(b) 1
(c) 0
}
equals
(d) None of these