Algebra 2

Two distinct numbers a and b are chosen randomly from the set {2, 22, 23, 24, ......, 225}. Find the probability that logab is an integer.

5 Answers

591
Akshay Ginodia ·

31/150

1133
Sourish Ghosh ·

No. of ways of selecting a and b is 25C2.2! = 600
No. of ways in which a and b can be chosen such that logbloga is an integer:
[251] - 1 + [252] - 1 + [253] - 1 + [254] - 1 + .... + [2525] - 1 = 62, where [.] is the floor function.
Probability = 62/600 = 31/300

865
Soumyadeep Basu ·

Yes, 31150.

1357
Manish Shankar ·

Answer is 31/300

535
Aditya Agarwal ·

Why are we permuting?

for eg. if a = 8 and b = 64
logab=2 but for the other case where a=64,b=8 value of the log becomes 0.5?

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