Can you explain the relationship?

Question

Explain the relationship between f(x)=3^x and log 3 ( the three is in the bottom) x

Answer 1

They are inverse functions. This means that when g(x) = log₃ x and f(x) = 3^x, you have both

 

f(g(x)) = x  and  g(f(x)) = x  true for all possible domain values for x in each equation.

 

Another way to putting this is: 3^log₃x = x for all positive real numbers x and log₃ 3^x = x for all real numbers x.