Question

How do you graph `y=log_4x`?

Answer 1

See below:

Explanation:

Graphs of log and ln are all roughly similar - they have a negative asymptote as it approaches 0 from the right, no negative values, and the graph slowly heads off towards infinity. The key is to find a value or two of `(x,y)` that can anchor the graph and make it useful.

What might those values be here?

We know that `y=log_4x` is the same expression as `4^y=x`. We need `x>0`, so let's see what we can do with `x=1` - that gives us `y=0`. We also can have `(4,1)`

And so the graph will look like this (this is `y=log_10x`) with the points `(1,0),(10,1)`:

graph{logx [-10, 10, -5, 5]}

but in our case it'll have the points `(1,0),(4,1)`, as seen in this short video (sorry, but I don't know how to do it with the Socratic graphing tool!):

graphing of log_4x