what is the relationship between

Question

what is the relationship between f(x)=b^x  and g(x)=log_b(x)? Assume that b is a positive real number and not equal to 1.

Answer 1

These 2 functions are inverses of each other. Look at f(g(x)), and also g(f(x)). Note that:

 

log_b (b^x)= x

 

and similarly,

 

b^log(x)= x

 

- Ben

Answer 2

In f(x), "b" is a factor, a multiplier.

In g(x), "b" is the base that is raised to a power, b^g(x) = x. b is the number that get repeatedly multiplied.