+367 Question 1.
Find x such that \(\log_x 81=\log_2 16\).
Question 2.
Suppose that f(x) and g(x) are functions on \(\mathbb{R}\) such that the range of f is [-5, 3], and the range of g is [-2, 1]. The range of \(f(x) \cdot g(x)\) is [a, b]. What is the largest possible value of b?
+506 Question 1:
\(\log_216\) is equal to 4, because \(2^4=16\).
So now, we are trying to find what x satisfies \(x^4=81\), so \(\boxed{x=3}\).
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 \(-5\cdot-2=\boxed{10}\)
