Question

How does $f(x)=\log _{x}(2)$ compare with $g(x)=\log _{2}(x) ?$ Here is one way to find out. a. Use the equation $\log _{a} b=(\ln b) /(\ln a)$ to express f(x) and g(x) in terms of natural logarithms. b. Graph f and g together. Comment on the behavior of f in relation to the signs and values of g.

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 3**a)**
When we use given equation we can express our functions in this way:

$\begin{aligned} f(x)&=\log_x2=\frac{\ln2}{\ln x} \\ \\ g(x)&=\log_2x=\frac{\ln x}{\ln 2} \\ \end{aligned}$

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