AMCAT Previous Years Questions on Logarithms



Topics
Sub- Topics
Expected Ques
Basic Mathematics
       6 – 8 Questions
Applied Mathematics
      8 – 10 Questions
Engineering Mathematics
       8 – 10 Questions

Question 1. log xY = 100 and log x2 = 10, then the value of y is
A. 2^10
B. 2^1000
C. 2^100
D. 2^10000

Correct Op: B

Question 2. What is the value of log(ab^2) – log(ac) + log(abc^4) – 3log(bc)?
A. 2
B. 0
C. -2
D. 1

Correct Op: D

Question 3
The value of log 9/8 – log 27/32 + log3/4 is ?
A. 0
B. 1
C. 2
D. 3

Correct Op: A
Given Exp. = log [{(9/8) / (27/32)} x 3/4)] = log [(9/8) x (3/4) x (32/27)] = log 1 = 0
 
Question 4
The simplified form of log(75/16) -2 log(5/9) +log(32/343) is ?
A. log 2
B. 2 log 2
C. log 3
D. log 5

Correct Op: A
Given Exp. = log75/16 – 2 log5/9 + log32/343 = log [(25 x 3) / (4 x 4)] – log (25/81) + log [(16 x 2) / (81 x 3)] = log(25 x 3) – log ( 4 x 4 ) – log(25) + log81 + log(16 x 2) -log (81 x 3) = log 25 + log 3 – log 16 – log 25 + log 81 + log 16 + log 2 – log 81 – log 3 = log 2
 
Question 5
Find the value of log (a^2 / bc) + log (b^2 / ac) + log (c^2 / ab) ?
A. 0
B. 1
C. abc
D. ab^2c^2
Correct Op: A
 
Question 6
The equation loga (x) + loga (1+x)=0 can be written as ?
A. x^2 + x – 1 = 0
B. x^2 + x + 1 = 0
C. x^2 + x – e = 0
D. x^2 + x + e = 0
Correct Op: A
 
Question 7
If 10^0.3010 = 2, then find the value of log0.125 (125) ?
A. 699 / 301
B. – 699 / 301
C. – 1
D. – 2
Correct Op: B
 
Question 8
log10 (10) + log10 (100) + log10 (1000) + log10 (10000) + log10 (100000) is equal to ?
A. 15
B. log 11111
C. log10 (1111)
D. 14 log10 (100)
Correct Op: A
1 + 2 + 3 + 4 + 5 = 15
 
Question 9
The value of log2 (1/64) is?
A. 6
B. – 6
C. 7
D. None of these
Correct Op: B
 
Question 10
If log 125 / log 5 = x, then x is equal to ?
A. 2
B. 3
C. 4
D. 1 / 2
Correct Op: B
If log 125 / log 5 = x then x = 3log5 / log5= 3