y=log5(x-1) Find the domain and range of each.

do you have a graphing calculator?

I have an app on my phone that is.

So your using your phone right now? Because the easiest way to find domain and range is by graphing it.

I am usually a proponent of graphing , but in this case, you should know that: log (STUFF) ... well "stuff" can never be zero or less than zero. Since "stuff" = x-1 that means that \(x-1 \geq 0\) That is your domain. The range is all y values. log base whatever has range from - infinity to positive infinity.

The domain would be 1 as the answer right? And range I can put any number? Is that what your saying?

Domain would be \[[1,\infty)\] and range would be \[(-\infty,\infty)\]

Thanks!

>The domain would be 1 as the answer right? And range I can put any number? Is that what your saying? Domain = INPUT = "values of x" Range = OUTPUT = "values of y" You choose values of x, you get values of y. Not the other way around. :)

Thanks! :) So in another problem like f(x)=ln(x+3)+2 Would the Domain be -1? Or no solution?

same thing. ln must be greater than zero. so you do \[x + 3 \gt 0\] Therefore \[x \gt -3\] so the domain would be \[(-3,\infty)\] Range is \[\mathbb{R}\]

But what about the 2? And isnt domain x>0 for logs? So therefore it would be no solution for -3?

but this log is shifted to the left by 3 units.. so if you have a number greater than -3 for example -2 then you would get \[\ln (-2 + 3) + 2\] Which is \[\ln (1) + 2\] The number inside the natural log cannot be 0 or negative

This is what the graph looks like

Thanks!

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