Probably Algebra!

Probability Level 3

Two distinct numbers a and b are chosen randomly from the set { 2 , 2 2 , 2 3 , . . . , 2 25 } \{2, 2^2, 2^3, ..., 2^{25}\} .

What is the probability that l o g a b \mathrm{log}_a b is an integer?

Probably Number Theory

7 50 \frac{7}{50} 31 300 \frac{31}{300} 1 2 \frac{1}{2} 13 100 \frac{13}{100} 2 25 \frac{2}{25}

Harsh Shrivastava by Harsh Shrivastava , 17, India

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1 solution

X X
Jul 13, 2018

Same probability as c d \frac cd is an integer,where c , d c,d are integers and 1 ≤ c ≤ 25 , 1 ≤ d ≤ 25 1\le c\le25,1\le d\le25

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