Question

What is the domain of the function h(x)=4log_5(x−6)+1 ? Enter your answer in the box.

All real numbers greater than______

Answer 1

All real numbers greater than 6.

Explanation:

To find the domain we have to find if there are intervals where the function is not defined.

In this case, we have a logarithm.

Logarithms of any base are not defined for 0 or values less than zero (negative numbers). So the logarithm argument must be greater than zero.

For the above to be true:
`x-6` must be greater than zero.

`x-6` > 0

`x` > 6

If x is greater than 6, the argument of the logarithm will be greater than zero and the function will be defined.

The anser is: All real numbers greater than 6.

Answer 2

The domain is all real numbers greater than 6

log functions cannot be less than 0