2019/20 AHSMC Part 1 Problem 6

Problem 6 of 16

Consider $a = 2^{1000}$ , $b = 3^{600}$ , and $c = 10^{300}$ . Which of the following is true?

Show solution

Solution

We have $a = 2^{1000} = (2^{10})^{100} = 1024^{100}$ , $b = 3^{600} = (3^6)^{100} = 729^{100}$ , and $c = 10^{300} = (10^3)^{100} = 1000^{100}$ . We have $729 < 1000 < 1024$ , and hence $b < c < a$ . The answer is (D).

University of Alberta

Answer choices

Solution