Question 1.
Find x such that logx81=log216.
Question 2.
Suppose that f(x) and g(x) are functions on R such that the range of f is [-5, 3], and the range of g is [-2, 1]. The range of f(x)⋅g(x) is [a, b]. What is the largest possible value of b?
Question 1:
log216 is equal to 4, because 24=16.
So now, we are trying to find what x satisfies x4=81, so x=3.
Question 2:
For the biggest value of b, we need to find 2 values in the ranges of f(x) and g(x) that, when multiplied together, results in the biggest possible result. That would be −5⋅−2=10