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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?

 Jan 21, 2021
 #1
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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 \(-5\cdot-2=\boxed{10}\)

 Jan 21, 2021
edited by textot  Jan 21, 2021
edited by textot  Jan 21, 2021
 #2
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Thank you so much for your help. I can comprehend these questions so much better now. Thank You!!!

 Jan 21, 2021

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