Logarithm- Aptitude Questions and Answers

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What is the solution of the equation xlog10(10/3) + log103= log10(2 + 3x ) + x ?

A)

10


B)

3


C)

1


D)

0



Correct Answer :

0


Explanation :

xlog10(10/3) + log103= log10(2 + 3x ) + x
log10(10/3)x + log103= log10(2 + 3x ) + log1010x [ because logaa =1, log am = m log a]
log10(10/3)x * 3= log10(2 + 3x ) * 10x [ because logca + logcb = logcab ]
(10/3)x * 3= (2 + 3x ) * 10x
3*10x/3x = (2 + 3x ) * 10x
3*10x = 3x * 10x *(2 + 3x )
3 = 3x *(2 + 3x )

Let 3x = y Then 3 = y *(2 + y )
y2 + 2y - 3=0
( y + 3)( y - 1) = 0
y = -3, 1 that is 3x = -3, 1

consider 3x = 1 [3x ≠ -3]
3x = 10
Hence x = 0

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The value of log23 x log 32 x log34 x log43 is ?

A) 1
B) 2
C) 3
D) 4

Correct Answer :

1


Explanation :

logax = logb x/logb a=log x/log a

Thus, log23 x log 32 x log34 x log43
=> (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4)
=> 1

The value of log 9/8 - log 27/32 + log3/4 is ?

A) 0
B) 1
C) 2
D) 3

Correct Answer :

0


Explanation :

loga(xy) = loga x + loga y
loga (x/y) = loga x - loga y
loga 1 = 0

Thus, log 9/8 - log 27/32 + log3/4 => log [(9/8) /(27/32)] + log3/4
=> log 4/3+ log3/4
=> log [(4/3)*(3/4)]
=> log 1
=> 0

The equation logax + loga (1+x)=0 can be written as ?

A) x2 + x - 1 = 0
B) x2 + x + 1 = 0
C) x2 + x - e = 0
D) x2 + x + e = 0

Correct Answer :

x2 + x - 1 = 0


Explanation :

loga(xy) = loga x + loga y
loga 1 = 0

So, logax + loga(1+x) = 0
⇒ logax (x+1) = loga1
⇒ x(x +1) = 1
⇒ x2 + x - 1 = 0

if log 3 = 0.477 and (1000)x = 3, then x equals to ?

A) 0.159
B) 10
C) 0.0477
D) 0.0159

Correct Answer :

0.159


Explanation :

loga(xp)=p(logax)
logx x=1

(1000)x = 3
⇒ log10103x = log103
⇒ 3x = log103
⇒ x = log103 / 3 = 0.477 / 3 = 0.159

Find the value of log9 81 - log4 32 ?

A) 1 / 2
B) - 3 / 2
C) - 1 / 2
D) 2

Correct Answer :

- 1 / 2


Explanation :

logax = logb x/logb a=log x/log a.
loga(xp)=p(logax)

log9 81 - log4 32
=> log32 34 - log22 25
=>(log 34 / log 32) - ( log 25/ log22)
=>(4 log 3 / 2 log 3) - ( 5 log 2 / 2 log2)
=> 4/2 - 5/2
=> -1/2

log-1/3 81 is equal to ?

A) - 27
B) - 4
C) 4
D) 127

Correct Answer :

- 4


Explanation :

logx x=1

y=xx is equivalent to, logxy = logxx ⇒ logxy =x

Let, log-1/381 = x
⇒ 81 = (-1/3)x
⇒ 34 = (-1/3)x = 3-x
⇒ x = -4

The value of log10 0.000001 is ?

A) 6
B) - 6
C) 5
D) - 5

Correct Answer :

- 6


Explanation :

log10 10-6 = -6

The value of log6 log5 15625 is ?

A) 1
B) 2
C) 3
D) 4

Correct Answer :

1


Explanation :

log6 log515625 = log6 log5(5)6
= log66(log55) = 1

If log10000x = -1/4, then x is ?

A) 1 / 100
B) 1 / 10
C) 1 / 20
D) 1

Correct Answer :

1 / 10


Explanation :

log104x = -1/4
⇒ x = (104)-1/4
= 1/10

Given that log10 2 = 0.3010 the value of log10 5 is ?

A) 0.3241
B) 0.6911
C) 0.6990
D) 0.7525

Correct Answer :

0.6990


Explanation :

log105 = log10(10/2)
= log1010 - log102
= 1-0.3010
= 0.6990

The value of log 128 - log 8 / log 4 is ?

A)
7

B)
5

C)
2

D)
1


Correct Answer :

2


Explanation :

log 128 - log 8 / log 4
=> log (128/8) / log 4
=> log 16 / log 4
=> log 42 / log 4
=> 2 log 4 / log 4
=> 2

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