Logarithm
Exam Duration: 45 Mins Total Questions : 25
Find the logarithm of 1728 to he base 2\(\sqrt { 3 } \).
- (a)
3.124
- (b)
3.1732
- (c)
6
- (d)
5
If logx \(\frac { 9 }{ 16 } =-\frac { 1 }{ 2 } ,\)then x is
- (a)
\(-\frac { 1 }{ 2 } \)
- (b)
\(\frac {2 }{3 } \)
- (c)
\(\frac { 81 }{ 256 } \)
- (d)
\(\frac { 256 }{81 } \)
The value of 3 log 3 +2 log 2 is
- (a)
log 108
- (b)
log 106
- (c)
log 109
- (d)
None of these
The true statement of the following is
- (a)
log (xy)=log x log y
- (b)
log (xy) = log x + log y
- (c)
Botha (a) and (b)
- (d)
None of these
One is the value of
- (a)
log102
- (b)
log10 100
- (c)
log10 10
- (d)
log10 1000
The value of [log2 log2 log2 (65536) is
- (a)
8
- (b)
16
- (c)
4
- (d)
1
logx x is equal to
- (a)
\(\frac { X }{ { log }_{ e }Y } \)
- (b)
\(X{ log }_{ e }Y\)
- (c)
\(\frac { { log }_{ e }X }{ { log }_{ e }Y } \)
- (d)
\(\frac { { log }_{ e }Y }{ { log }_{ e }X } \)
log10 10+ log10 100+ log10 1000+ log10 10000+ log10 100000 is
- (a)
23
- (b)
15
- (c)
21
- (d)
13 log10100
The value of \(\left( \frac { 1 }{ 3 } { log }_{ 10 }\quad 125-2{ log }_{ 10 }\quad 4+{ log }_{ 10 }\quad 32 \right) is\)
- (a)
\(\frac { 4 }{ 3 } \)
- (b)
3
- (c)
1
- (d)
7
The value of logy X. logz Y . logX Z is
- (a)
log xyz
- (b)
xyz
- (c)
1
- (d)
0
The value of \(\frac { 1 }{ { log }_{ xy }(XYZ) } +\frac { 1 }{ { log }_{ yz }(XYZ) } +\frac { 1 }{ { log }_{ zx }(XYZ) } is\quad equal\quad to\)
- (a)
XYZ
- (b)
2
- (c)
0
- (d)
1
If log4 x + log2 x -6 then the value of 'x' is
- (a)
16
- (b)
4
- (c)
2
- (d)
1
log1/3 81 is equal to
- (a)
9
- (b)
27
- (c)
-4
- (d)
4
Give log10 2= 0.3010, the value of log10 5 is
- (a)
0.6990
- (b)
0.6919
- (c)
0.6119
- (d)
0.7525
If loga X=m, the value \({ log }_{ n }^{ 2 }\) X is
- (a)
\(-\frac { 1 }{ m } \)
- (b)
m
- (c)
m/2
- (d)
None of these
(log tan10 log tan 20 ...log tan 500) is
- (a)
1
- (b)
-1
- (c)
0
- (d)
\(\frac { 1 }{ \sqrt { 2 } } \)
The value \(\frac { 1 }{ 1+{ log }_{ x }(YZ) } +\frac { 1 }{ 1+{ log }_{ y }(XY) } +\frac { 1 }{ 1+{ log }_{ z }(XY) } is\)
- (a)
1
- (b)
\(\frac { 1 }{ { XY }^{ 2 } } \)
- (c)
X=Yz
- (d)
0
Give that log103=0.3010, log103=0.4771 and log107=0.8491 then log10\(\frac { 108 }{ \sqrt { 7 } } \)is
- (a)
2.6123
- (b)
1.6088
- (c)
1.6320
- (d)
2.4558
Which is not correct?
- (a)
log10(1+2+3)=log10(1:2:3)
- (b)
log101=0
- (c)
log10 (2+3)=log10 2:3
- (d)
log1010=1
If a, b, c are three consecutive integers,, then log(ac+1) is equal to
- (a)
log(2b)
- (b)
x =2
- (c)
2 log b
- (d)
None of these
The solution of equation log7 [log4(X2)]=0 is
- (a)
x=1
- (b)
x=2
- (c)
x=\(\pm \)2
- (d)
x=-2
If log r p=2, logr q=3, then the value of logp q is equal to
- (a)
1/3
- (b)
2/3
- (c)
3/2
- (d)
6
If log X2 Y2=a, and log\(\frac { X }{ Y } \)=b,then \(\frac { logX }{ logY } \)is equal to
- (a)
\(\frac { a-3b }{ a+2b } \)
- (b)
\(\frac { a+3b }{ a-2b } \)
- (c)
\(\frac { a+2b }{ a-3b } \)
- (d)
\(\frac { a-2b }{ a+3b } \)
If 22x+3=6x-1,equals to
- (a)
\(\frac { 4log\quad 2\quad +log3 }{ log3-log2 } \)
- (b)
\(\frac { 3log2+log3 }{ lo3-2log2 } \)
- (c)
\(\frac { log\quad 48 }{ log\quad 7 } \)
- (d)
None of these
The value of \({ log }_{ 3 }\left( 1+\frac { 1 }{ 3 } \right) +{ log }_{ 3 }\left( 1+\frac { 1 }{ 4 } \right) { log }_{ 3 }\left( 1+\frac { 1 }{ 5 } \right) +......+{ log }_{ 3 }\left( 1+\frac { 1 }{ 24 } \right) is\)
- (a)
-1+2log35
- (b)
2
- (c)
3
- (d)
4
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