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I'm trying to graph $f(x,y)=\ln(x)-y$, however, I am not sure how as all of my tools are refusing to graph it.

Can you please help me?

Thanks

Peter
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    What do you mean by the graph of $\ln(x) - y$? Do you mean $z = \ln(x) - y$, $0 = \ln(x) - y$, some other constant $c = \ln(x) - y$? It doesn't make sense to just graph $\ln(x) - y$ because you need an equation $(=)$ to be able to graph something. – DMcMor Feb 16 '21 at 15:04
  • @DMcMor Sorry, I meant $f(x,y)=ln(x)-y$ – Peter Feb 16 '21 at 15:07
  • So since it is a function from $\mathbb{R}^2$ to $\mathbb{R}$, you want a $3$D representation of the graph ? – TheSilverDoe Feb 16 '21 at 15:12
  • It really depends on the tools you have available. In Mathematica, for example, you would use Plot3D. – rogerl Feb 16 '21 at 15:12
  • @TheSilverDoe Only in 2D with $x$ and $y$ axes. – Peter Feb 16 '21 at 15:13
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    @Peter You cannot draw it in 2D! You have two input values $x$ and $y$ and so you need one more axis to represent the value of $f$. – VIVID Feb 16 '21 at 15:15

2 Answers2

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Note that there is no way to plot this in 2D because you would need an equation of the form $f(x,y) = 0$, and what you have is $f(x,y) = \ln(x) - y$, which can be thought of as $f(x,y) = z$. That means you need a 3D plot to visualize it.

There are several good online options for plotting 3D graphs. Here are two good ones:

1.) Calcplot3D, which produces the following plot. This one is my personal favorite, but you might want to see here for key commands for camera controls.enter image description here

2.) Geogebra, which produces the plot enter image description here

DMcMor
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You cannot draw it on the $Oxy$-plane. You have two input values $x$ and $y$ and so you need one more axis to represent the value of $f$. Below is the graph drawn via GeoGebra:

enter image description here

VIVID
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