What are the domain, range, x-intercept, and vertical asymptote of y=logₓ4?

[Erin_Sharpe]

y=logx4
state domain and range, x-intercept, vertical asymptote.

I have never seen a question like this before.

Please help me!

 

[arildno]

It might be easier to find what you're after by the rewriting:
$$x^{y}=4$$

 

[arildno]

Note that since for real exponents, the exponential is only defined for positive numbers, so the maximal domain for x is x>0.
Try and find out the range and where a vertical asymptote must be!

 

[dextercioby]

HINT:It may be much easier if u rewrote it:
$$y(x)=\frac{\ln 4}{\ln x}$$

Daniel.

 

[arildno]

Oops!
x=1 must be excluded from the domain!

 

[Erin_Sharpe]

:( this is so sad. because I completely don't understand this at all. it just makes absolutely no sense to me... is there any way it could be explained to me any easier?

 

[Erin_Sharpe]

vertical asymptote... 4? :s

 

[dextercioby]

What's the definition of a vertical asymptote...?

Daniel.

 

[arildno]

Erin sharpe:
Do you understand the transformation:
$$y=log_{x}4\to{x}^{y}=4\to{y}=\frac{ln(4)}{ln(x)}$$
(the last step was given by Daniel)