What's the point of using logarithms when sketching the inverse of a function?

by maki1995
Tags: function, inverse, logarithms, point, sketching
 P: 2 What's the point of logarithms when trying to sketch functions? Isn't y=3^x the same as x=3^y? I think it should be the same, but I get different results for each method. If it is the same, what's the point of y=log3x? It's confusing and I don't get the same results when trying to find the points in the graph. It makes sense when you try to solve an equation with different bases, but what's the point of logarithms when sketching graphs? For example, let's say you have y=3^x. The inverse function would be y=log3x or x=3^y. I'm trying to find the points for the graph of the inverse function. Let's say y=2. 2=log3x which means x would be 4.19. Now, for the other equation, if x=3^2, x would be 9, which doesn't make sense.
Engineering