Given the function f(x) = 0.3(4)^x, what is the value of f^-1(6)?

Solution:

Given the function f(x) = 0.3(4)^x

Let y = f(x) = 0.3(4)^x

Apply log on both sides

logy = (0.3)xlog(4)

logy = 0.3x(0.6)

logy = 0.18x

x = logy / 0.18 = f(y)

y = f^-1(x)

Swap the variables

f^-1(x) = logx /0.18

f^-1(6) = log6 / 0.18

f^-1(6) = 4.32

Given the function f(x) = 0.3(4)^x, what is the value of f^-1(6)?

Summary:

Given the function f(x) = 0.3(4)^x,the value of f^-1(6) is 4.32