Logarithmic function, all real numbers.

Question

Suppose f(x) is a function defined on all real numbers and that logbf(x)=3x. What is f(x) written explicitly? f(x)=b^3x

What is f(log_bx)?

 

Answer 1

Remember that in the log expression log_b y = x is the same as y = b^x. Therefore, log_b f(x) = 3x would mean that f(x) = b^3x.

 

f(log_bx) = b^3(log_bx)  because I am putting in log_bx for x in the b^3x function

b^log_bx =x; 

 

therefore, f(log_bx) = x³