# 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

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