What is the inverse of f(x)=log1/5 x

Question

?(1 point)
f^−1(x)=

Answer 1

To find the inverse of the function \( f(x) = \log_{1/5}(x) \), we can follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = \log_{1/5}(x) \]

2. Rewrite the logarithmic equation in exponential form: \[ x = (1/5)^y \]

3. To isolate \( y \), take the reciprocal of the base: \[ x = 5^{-y} \]

4. Solve for \( y \): \[ -y = \log_{5}(x) \] \[ y = -\log_{5}(x) \]

5. Therefore, the inverse function, denoted \( f^{-1}(x) \), is: \[ f^{-1}(x) = -\log_{5}(x) \]

So, the final answer is: \[ f^{-1}(x) = -\log_{5}(x) \]