Given the function f(x) = 0.5(3)^x, what is the value of f^-1(7)?

Solution:

Given function is

f(x) = 0.5(3)^x,

Let f(x) = y = 0.5(3)^x,

3^x = 2y

x = ln(2y)/log 3 = f(y)

Swap the variables

y = ln(2x)/log 3 = f^-1(x)

f^-1(7) = ln(2(7))/ log 3

= ln(14)/ log 3

Therefore, f^-1(7) = ln(14)/ ln(3)

Given the function f(x) = 0.5(3)^x, what is the value of f^-1(7)?

Summary:

Given the function f(x) = 0.5(3)^x, the value of f^-1(7) is ln(14)/ log 3.