Question

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

y = logo6x
y = logx6
y =log 1/6x
y=log6 6x

Answer 1

It is the 1 one because it is

Answer 2

The first choice,
`y = \log_6x`.

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`.