Skip to main content

AMC 12 Mock Exam 5 Problem 6

Problem 6 of 25

Real numbers aa and bb satisfy 2a=32^a=3 and 3b=163^b=16. What is the value of abab?

Answer choices

Show solution

Solution

From 2a=32^a=3 we get 2ab=(2a)b=3b=16=242^{ab}=(2^a)^b=3^b=16=2^4, so ab=4ab=\boxed{4}.

Tagged: logarithms, change of base