Question

which logarithmic function is represented by the exponential function $f(x)=x^{10}$?$log_{x} f(x) = 10$$log_{10} f(x) = x$$log_{10} f(x) = 10$$log_{x} f(x) = x$

Explanation:

Step1: Recall log-exponential conversion

For $b^y = x$, $\log_b x = y$.

Step2: Match given function to form

Given $f(x) = x^{10}$, here $b=x$, $y=10$, $x=f(x)$.

Step3: Apply conversion rule

Substitute into $\log_b x = y$: $\log_x f(x) = 10$.

Answer:

$\log_x f(x) = 10$