which of the following is the inverse of $y = 6^{x}$?\n$y=log _{6}x$\n$y=log _{x}6$\n$y=log…

which of the following is the inverse of $y = 6^{x}$?\n$y=log _{6}x$\n$y=log _{x}6$\n$y=log _{\frac{1}{6}}x$\n$y=log _{6}6x$

which of the following is the inverse of $y = 6^{x}$?\n$y=log _{6}x$\n$y=log _{x}6$\n$y=log _{\frac{1}{6}}x$\n$y=log _{6}6x$

Answer

Explanation:

Step1: Recall the definition of inverse functions

For (y = a^{x}), its inverse function is (y=\log_{a}x) (by the relationship between exponential and logarithmic functions: if (y = a^{x}), then (x=\log_{a}y), and when finding the inverse, we swap (x) and (y)).

Step2: Identify (a) in the given function

In the function (y = 6^{x}), (a = 6).

Answer:

A. (y=\log_{6}x)