Question

How do you find the domain and range of `y = log_5x`?

Answer 1

`f(x) = log_5 x` is the inverse of the function `e(x) = 5^x`
which has domain `(-oo, oo)` and range `(0, oo)`.

So the domain of `log_5 x` is `(0, oo)` and range is `(-oo, oo)`

Explanation:

The domain of `e(x) = 5^x` is the whole of `RR`, that is `(-oo,oo)`, but its range is `(0, oo)`.

So the domain of its inverse `y = log_5 x` is `(0,oo)` and its range is `(-oo,oo)`