Question

What is the inverse of f(x)=log1/5 x
?(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:
\[
f^{-1}(x) = -\log_{5}(x)
\]