# Issue with logarithmic function

Enrico shared this problem 4 years ago
Not a Problem

The problem is that there shouldn't be the y intercept.

Let x=0

2^x-1 = 2^0-1 = 1-1 = 0

So the denominator should be Log10(0) which is impossible so y = 1/Log10(0) is impossible.

1

The point you displayed in your pic is just temporary.

Click on the function again or anywhere else in the Graphics View to make it disappear.

I understand that x=0 is the lower bound of the domain of the function. But it isn't possible to exclude x=0 from the graph, because of the density of points in the plot of a function.

I also understand that it's not great from a visual point of view, but f(0) gives 0, which is "numerically" correct, despite f(0) is not an evaluation of the function, but a limit.

So I guess that there are no problems with your function, unless you've got any other result that is not mathematically correct.

1

Log(0) is not impossible. It's a huge negative number. lim(x->0+) log(x) = - infinity

1

Hello Enrico!

You are right, but sometimes GeoGebra think and behaves like HAL9000. :-)

For you there is a gap at 0, but this gap can be closed because f(x)=1/(lg(2^x-1) is continuous continuable.

In the same way GeoGebra closes the gap at e. g. 1 for g(x)=(x^2-2*x+1)/(x-1).

So GeoGebra gives you the value of the continuuos extension of your function and it's not a special issue of e. g. the logarithmic function.

Kind Regards

mire2