1. ## Determining Quadrants of Logarithmic Function

How can I determine what quadrants $\displaystyle y = log_4(x)$ lies in?

I know that this is equivalent to $\displaystyle 4^y = x$ but is there a way I can put that into terms of y so I can plug it into the graphing calculator?

Thanks!

2. Why not use the change of base rule?

$\displaystyle y = \dfrac{\log_e(x)}{\log_e(4)}$

3. Originally Posted by mathguy20
How can I determine what quadrants $\displaystyle y = log_4(x)$ lies in?

I know that this is equivalent to $\displaystyle 4^y = x$ but is there a way I can put that into terms of y so I can plug it into the graphing calculator?

Thanks!
$\displaystyle y = \log_b{x}$ has domain $\displaystyle x > 0$ and a range of all real numbers ... what quadrants would that be?

for graphing purposes, note the change of base formula ...

if $\displaystyle y = \log_b{x}$ , then $\displaystyle y = \frac{\log(x)}{\log(b)}$

... where log is base 10 or base e (your choice on the calculator)

also, note that the new operating system for the TI-84 will graph logs for any base.

4. Thanks for the help -- I understand it now.

And I just updated the OS on my TI-84 as well. Thanks for letting me know about that!