# How do you graph y=log_4x?

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 $\left(x , y\right)$ that can anchor the graph and make it useful.

What might those values be here?

We know that $y = {\log}_{4} x$ 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 $\left(4 , 1\right)$

And so the graph will look like this (this is $y = {\log}_{10} x$) with the points $\left(1 , 0\right) , \left(10 , 1\right)$:

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

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