How to Graph Parent Functions and Transformed Logs
Want some good news, free of charge? Graphing parent functions and transformed logs is a snap! You can change any log into an exponential expression, so this step comes first. You then graph the exponential, remembering the rules for transforming, and then use the fact that exponentials and logs are inverses to get the graph of the log.
How to graph a parent function
Exponential functions each have a parent function that depends on the base; logarithmic functions also have parent functions for each different base. The parent function for any log is written f(x) = log_{b} x. For example, g(x) = log_{4} x corresponds to a different family of functions than h(x) = log_{8 }x. This example graphs the common log: f(x) = log x.

Change the log to an exponential.
Because f(x) and y represent the same thing mathematically, and because dealing with y is easier in this case, you can rewrite the equation as y = log x. The exponential equation of this log is 10^{y} = x.

Find the inverse function by switching x and y.
You find the inverse function 10^{x} = y.

Graph the inverse function.
Because you’re now graphing an exponential function, you can plug and chug a few x values to find y values and get points. The graph of 10^{x} = y gets really big, really fast. You can see its graph in the figure.
Graphing the inverse function y = 10^{x}.