Question

How do you find the domain and range of `log_(6) (49-x^2)`?

Answer 1

The argument of a `log` function must be positive.

Explanation:

So
`49-x^2>0->x^2<49`

This only happens if
`-7 < x<+7` this is the domain

Range:
With `x` nearing `+-7` the argument `49-x^2` will be nearing `0` and the `log` itself will go to `-oo`

Or, in the language:
`lim_(x->+-7) log_6 (49-x^2)=-oo`

The top of the range is when the argument is maximal, this means when `x=0`, the max value will be:
`log_6 49=log_10 49/log_10 6~~2.172`
graph{log(49-x^2)/log(6) [-12.33, 12.99, -7.11, 5.55]}