Question

Which of the following is the inverse of y=6*?

Answer 1

Answer:

The first choice, $y = \log_6x$.

Step-by-step explanation:

$\log_b{x}$ is logarithm of $x$ to the base $b$ (the base must be positive.) Raising the base $b$ to a power of $\log_b{x}$ would give $x$. In other words,  $b^{\log_b{x}} = x$.

If $f^{-1}$ is indeed the inverse of the function $f$, then $f^{-1}(f(x)) = x$. Apply this property of inverse functions to check each option. By the logarithm property (in this case if $b = 6$,) $6^{\log_6{x} = x$. In other words, the first choice is indeed the inverse of $f(x) = 6^x$.

Answer 2

It is the 1 one because it is