Logarithm- Aptitude Questions and Answers

View in English View in Hindi

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

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

Latest Updates

Physics

Atmospheric pressure at sea level equals ?

General Knowledge of India

Which of the following dance forms was introduced by the great Vaishnava saint and reformer Mahapurusha Sankaradeva ?

Which of the following is the only classical dance of india having links with Muslim culture and represents a unique synthesis of Hindu and Muslim genius in art ?

Time and Distance

Starting from the same point at the same time, Ruhan and Yuvan had to reach the same destination. While Ruhan drove at 45 km/hr, Yuvan was slower by 5 km/hr. If Yuvan arrived at the destination an hour after Ruhan did, the distance covered by each, in Kilometres, was ?

Simple Interest

A sum of money was invested at a certain rate of simple interest for 4 years. Had the sum been invested at a rate 3% higher than the actual rate, the interest earned would have been 720 Rs more. Find the sum initially invested?

Ratio and Proportion

A bag contains red, blue and black balls. The ratio of red to blue balls is 3 : 5. The ratio of black to red balls is 3 : 4. What is the ratio of blue to black balls?

Profit and Loss

Selling a pack of incense sticks for 136 Rs resulted in a loss of 15%. To make a profit of 10%, the selling price should be ?

Percentage

23% of a bucket full of diluted milk was water. If the quantity of pure milk in the bucket was 15.4 liter, then the capacity of the bucket was ?

Average

The average of the marks obtained by three girls in a test was twice the average of the marks obtained by eight boys in that test. If the total marks obtained by all these examinees was 168, find the average marks each of the girls obtained ?

Pipes and Cistern

44 pipes can fill a large water tank in 27 hours. How many hours it take for 66 pipes to fill four such tanks ?

HCF and LCM

A natural number, when divided by 3, 4, 5, 6, and 7 respectively, leaves corresponding remainder of 2, 3, 4, 5 and 6. What is the smallest of all such numbers fulfilling the above condition ?

Coding-Decoding

If in a certain code language, PRINT is written as 34825 and TRUE is written as 5479. Then, how will TENURE be written in that language?

Order Sequence

Arrange the given words from smallest to biggest-
1.Jug
2.Mug
3.Bucket
4.Drum
5.Cup

Statement and Conclusion

Statements
All socks are shoes
Some shoes are black

Conclusions
I. Some shoes are socks.
II. No scoks is black

Numbers

The difference between the place value of 4 and 2 in the number 833749502 is ?

Analogy

GIKM : HJLN :: PRTV : .........?

Order Sequence

In a row of girls, Nanda is eighth from the left and Chanda is nineteenth from right. When Nanda and Chanda interchange their positions, Chanda becomes twnty-third form right. How many girls are there in the row?

Analogy

Summer: Day :: Winter : ........?