What does this graph look like? $y = \log_x{2}$

Question

The equation is $y = \log_x{2}$, where x is the variable and the base of the logarithm. What does the graph look like?

In general, what does $y = \log_x{k}$ look like, where k is some real constant?

I cannot plug this into online graphers like fooplot.com because they don't seem to have a notation that allows putting x in the base of a logarithm.

Answer 1

Try this Graphing calculator..Type this log_x2 into it. Here's the graph

Note the graph is basically..$$f(x)=\frac{\ln2}{\ln x}\approx\frac{0.69314718056}{\ln x}$$

and an asymptote at $x=1$.

Answer 2

$$y(x)=\ln_x(2)=\frac{\ln(2)}{\ln(x)} \qquad \text{and more generally}\quad \ln_x(k)=\frac{\ln(k)}{\ln(x)} $$

Answer 3

There are 2 cases. I changed your parameter from $x$ to $a$

I hope this makes sense. If the base is from $0<a<1$ and the argument is variable it is Graph 1. If the base is from $1<a<infinity$ and the argument is variable it is Graph 2.