This set of Aptitude Questions and Answers (MCQs) focuses on “Functions – Set 2”.
1. Which value of z would satisfy 5z+3 = 5z+2?
a) log (25 / 4) / log (9 / 4)
b) log (4 / 25) / log (9 / 4)
c) log (4 / 125) / log (5 / 2)
d) log (125 / 5) / log (4 / 2)
View Answer
Explanation: Given,
5z+3 = 5z+2
➩ log (5z+3) = log (5z+2)
➩ (z + 3) log 5 = (z + 2) log 2
➩ z log 5 + 3 log 5 = z log 2 + 2 log 2
➩ z log 5 – z log 2 = 2 log 2 – 3 log 5
➩ z = ( 2 log 2 – 3 log 5) / (log5 – log 2)
➩ z = log (22 / 53) / log (5 / 2)
➩ z = log (4 / 125) / log (5 / 2)
2. What will be the value of log10 (xayb) if log10x = a and log10y = b?
a) a2 + b2
b) 2a / 3b
c) 2a3 + 2b3
d) a2 / b3
View Answer
Explanation: Given,
log10 (xayb)
➩ log10 (xayb) = log10xa + log10yb
➩ log10 (xayb) = a log10x + b log10y
➩ log10 (xayb) = a2 + b2
3. If log 3 log (3p – 2) and log (3p + 4) are in arithmetic progression, then what will be the value p?
a) log 32
b) log 23
c) 8 / 3
d) 16 / 3
View Answer
Explanation: As the two terms are given in arithmetic progression thus,
log (3p – 2) – log 3 = log (3p + 4) – log (3p – 2).
➩ log (3p – 2) / log3 = log (3p + 4) / log (3p – 2)
➩ log 3p / log 2 log 3 = p log 3 log 4 log 2 / p log 3
➩ p log 3 / log 2 log 3 = p log 3 log 4 log 2 / p log 2
➩ p / log 2 = log 4 log 2
➩ p = log 8
➩ p = log 23
4. Which value of a would satisfy (log2a)2 – log2a4 – 32 = 0 if, a is an integer?
a) 256
b) 1 / 16
c) 64
d) 144
View Answer
Explanation: Given,
(log2a)2 – log2a4 – 32 = 0
➩ (log2a)2 – 4 log2a – 32 = 0
Let, log2a = z
➩ z2 – 4z – 32 = 0
➩ z2 – 8z + 4z – 32 = 0
➩ z (z – 8) + 4 (z – 8) = 0
➩ (z – 8) (z + 4) = 0
➩ z = 8, – 4
According to the question,
➩ log2a = z
➩ log2a = 8 or – 4
➩ a = 28 or 2-4
➩ a = 256 or 1 / 16
As a is an integer thus, a = 256.
5. Which value of q will satisfy log3[log2(q2 – 4q – 37)] = 1 if q is a positive number?
a) 13
b) 5
c) 9
d) 16
View Answer
Explanation: Given,
log3[log2(q2 – 4q – 37)] = 1
➩ log2(q2 – 4q – 37) = 3
➩ q2 – 4q – 37 = 8
➩ q2 – 4q – 45 = 0
➩ q2 – 9q + 5q – 45 = 0
➩ q (q – 9) + 5 (q – 9) = 0
➩ (q – 9) (q + 5) = 0
➩ q = 9, – 5.
As q is a positive number, thus, q = 9.
6. Which f the following values of x will satisfy log5x – log5√x = 8 logx5?
a) 1 / 216
b) 1 / 25
c) 1 / 64
d) 1 / 625
View Answer
Explanation: We have,
log5x – log5√x = 8 logx5
➩ log5 (x / √x) = 8 / log5x
➩ log5 √x = 8 / log5x
➩ \(\frac {1}{2}\) log5x = 8 / log5x
➩ (log5x)2 = 16
➩ log5x = +4 or -4
Thus, x = 54 or 5-4
➩ x = 625 or 1 / 625.
7. What will be the value of log77 + log772 + log773 + ……… + log77n?
a) n (n + 1) / 2
b) n2 + 2n / 3
c) n – 1 / 3
d) n2 / 5
View Answer
Explanation: Given,
log77 + log772 + log773 + ……… + ➩ log77n
➩ log77 + 2log77 + 3log77 + ……. + nlog77
➩ 1 + 2 + 3 + ……. + n
➩ n (n + 1) / 2
8. What is the number of digits in 350?
a) 46
b) 23
c) 24
d) 47
View Answer
Explanation: We have,
350
⇒ log 350
⇒ 50 log 3
⇒ 50 * 0.4771
⇒ 23.855
⇒ characteristic = 23
Hence the number of digits will be 23 + 1 = 24.
9. Which of the following value of w is correct if, log100000w = – 1 / 5?
a) 10
b) 0.0001
c) 0.1
d) 0.001
View Answer
Explanation: Given,
log100000w = – 1 / 5
➩ w = (100000)-1/5
➩ w = (105)-1/5
➩ w = 10-1
➩ w = 1 / 10 = 0.1
10. Which of the following is the correct value of z given log2[log3 [log2(log2z)]] = 1?
a) 2512
b) 464
c) 512
d) 1024
View Answer
Explanation: Given,
log2[log3 [log2(log2z)]] = 1
➩ log2[log3 [log2(log2z)]] = 1
➩ log3[log2(log2z)] = 2
➩ log2(log2z) = 32 = 9
➩ log2z = 29 = 512
➩ z = 2512
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