I have no idea where to go with this. Looking for domain and range here too

Remember the definition of logarithm: y = log (base m) n. Logarithm of n to a base m is a number to which the base m must be raised to get n. I.e. m^y=n. From the definition you can get the idea of the range and domain. What you can say right away is that x > 0 and x cannot be 1.

Or you can derive the following identity which will make your life really easy:

log (base a) b = ( log (base c) b ) / (log (base c) a); here c > 0 and c is not 1.

Try to derive it yourself.

You can select your own new base, whatever you like most, e.g. c = 10 or c = e. For c = 10:

y = (log (base 10) 4) / (log (base 10) x) ---- from here, domain and range are easier to see.

Another way to plot your function is to plot the inverse function first and then mirror reflect it around the line y=x.