CAT 2020: Logarithm PDF Download

Q.1. If log₄ 5 = log₄ y log₆ √5 , then y equals

Ans: 36


⇒ y = 36

Q.2. If y is a negative number such that 2^{y2log₃ 5} = 5^{log₂ 3} , then y equals
(a) log₂(1 / 3)
(b) - log₂(1 / 3)
(c) log₂(1 / 5)
(d) - log₂(1 / 5)

Correct Option is A
2^{y2log₃ 5} = 5^{log₂ 3}

 ( is negative )

Q.3.  The value of , for 1 < a ≤ b cannot be equal to
(a) -0.5
(b) 1
(c) 0
(d) -1

Correct Option is B

= log_a a - log_ab +log_bb - log_ba
=
since ( log_ab + log_ab ) ≥ 2
∴ 1 can't be the answer.

Q.4.  equals

Ans: 24


= 24

Q.5. In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is
(a) 469
(b) 399
(c) 357
(d) 417

Correct Option is B
Let the total marks be T and scores of Bishnu, Asha and Ramesh be a, b and c respectively.
Given, a = 52% of T = c - 23 and b = 64% of T = c + 34
Hence, (64 - 52)% of T = (c + 34) - (c - 23) = 57
i.e. 12% of T = 57
Hence, score of Geeta = 84% of T = 7  x 57 = 399