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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

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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
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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