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

Indian Geography

What is the approximate distance between earth and the moon?

Indian History

In which year was the battle of ‘Koregaon Bhima’ fought?

The approach that is very useful in organizing the content in history is.

General Knowledge of India

NITI Aayog stands for _____.

General Knowledge of MP

India’s first Ramayan art museum was established at?

Errors Identification

Read the sentence carefully and choose the option that has an error in it:
The management’s trusted employee was suspected of stealing large sum of money.

Read the sentence carefully and choose the option that has an error in it:
The teacher asked the child to repeat again because he spoke feebly.

Fill in the blank

Fill in the blank with the most appropriate preposition in the given sentence.
Let’s sit _________ the shade of this beautiful tree.

Choose the most appropriate determiner for the given sentence.
________of what he said was very sensible.

Substitution

Choose the option that substitutes the given phrase appropriately.
A work of art made by carving

Correct sentence

Choose the option that best transforms the sentence into its Indirect form:
‘What country do you come from?’ said the police officer.

Alternative Phrase

Choose the option that best explains the highlighted expression:
All human beings have feet of clay.

Fill in the blank

Choose an appropriate modal for the given sentence:
My doctor said that I_____ stop smoking as one of my lungs got infected.

Choose the appropriate prepositions for the given sentence:
My parents have been married ________ forty-nine years, but you can still see the love ________ their eyes.

Choose the appropriate conjunction for the given sentence:
______ it rains, the college will declare the holiday.

Antonyms

Choose the appropriate antonym for the highlighted word in the given sentence.
The family protracted their visit by several days.

Tenses

Choose the appropriate tenses to fill in the blanks in the given sentence:
Please _________ a noise. Ritu __________ to sleep.

Synonyms

Choose the appropriate synonym for the highlighted word in the given sentence.
Does he really expect us to believe such a flimsy excuse?

Latest Job Notifications

Jobs in Bihar

बिहार तकनीकी सेवा आयोग / Bihar Technical Service Commission (BTSC) - 12771 पद - 01/09/2022 अंतिम तिथि

Jobs in Rajasthan

राजस्थान उच्च न्यायालय / Rajasthan High Court - 2756 पद - 22/09/2022 अंतिम तिथि

Jobs in Uttar Pradesh

उत्तर प्रदेश पावर कॉर्पोरेशन लिमिटेड / Uttar Pradesh Power Corporation Limited - 1033 पद - 12/09/2022 अंतिम तिथि

Jobs in Tamil Nadu

तमिलनाडु चिकित्सा सेवा भर्ती बोर्ड / Tamil Nadu Medical Services Recruitment Board (MRB) - 889 पद - 30/08/2022 अंतिम तिथि

Jobs in Andhra Pradesh

आंध्र प्रदेश स्वास्थ्य, चिकित्सा और परिवार कल्याण विभाग / Andhra Pradesh Health, Medical and Family Welfare Department - 1681 पद - 22/08/2022 अंतिम तिथि

SSC Recruitment

कर्मचारी चयन आयोग (एसएससी) Staff Selection Commission (SSC) - 4300 पद - 30/08/2022 अंतिम तिथि - CPO Recruitment

Banking Jobs

बैंकिंग कार्मिक चयन संस्थान Institute of Banking Personnel Selection(IBPS) - 6432 पद - 22/08/2022 अंतिम तिथि

बैंकिंग कार्मिक चयन संस्थान Institute of Banking Personnel Selection(IBPS) - 7855 पद - 29/07/2022 अंतिम तिथि

SSC Recruitment

कर्मचारी चयन आयोग (एसएससी) Staff Selection Commission (SSC) - 1411 पद - 29/07/2022 अंतिम तिथि

Jobs in Rajasthan

राजस्थान अधीनस्थ और मंत्रिस्तरीय सेवा चयन बोर्ड Rajasthan Subordinate and Ministerial Services Selection Board (RSMSSB) - 5546 पद - 22-Jul-2022 अंतिम तिथि