Question

For the functions f(x)=log3/5 and g(x) = log2(x), for what values of x is ƒ(x) > g(x)?A. 0 < x < 2B. 1 < x < ∞C. 0 < x < 1 D. 0

Answer 1

The two functions are given to be:

`\begin{gathered} f(x)=\log_{(3)/(5)}(x) \\ g(x)=\log_2(x) \end{gathered}`

We can plot a graph of the two functions using a graphing calculator, we can compare the functions:

The graph of f(x) is the red graph while g(x) is the blue graph.

We can see that the graph of f(x) is greater than the graph of g(x) from 0 up to 1, while g(x) is greater from 1 up to positive infinity.

Therefore, the interval where ƒ(x) > g(x) is:

[tex]0OPTION C is the correct option.