Question

Which function is the inverse of f(x)=log5 x
?(1 point)
Responses

f−1(x)=(1/5)x
f inverse of x is equal to 1 fifth to the x th power

f−1(x)=5^x
f inverse of x is equal to 5 to the x th power

f−1(x)=x^5
f inverse of x is equal to x to the 5th power

f−1(x)=x^1/5
f inverse of x is equal to x raised to the 1 fifth power

Answer 1

To find the inverse of the function \( f(x) = \log_5(x) \), we can use the fact that the logarithm function is the inverse of the exponential function.

The definition of \( f(x) = \log_5(x) \) means that:

\[
y = \log_5(x) \quad \text{is equivalent to} \quad x = 5^y
\]

To find the inverse \( f^{-1}(x) \), we switch \( x \) and \( y \):

\[
x = 5^y
\]

Now, solving for \( y \) gives us:

\[
y = 5^x
\]

Therefore, the inverse function is:

\[
f^{-1}(x) = 5^x
\]

So the correct choice among the options provided is:

**f−1(x)=5^x**
**f inverse of x is equal to 5 to the x th power**