Question

Kindly answer this question?

Answer 1

`-oo< x<1`

Explanation:

Solve the function for `y`: `y=log_a(a-a^x)`.

Since the logarithm can only accept values greater than `0`, `a-a^x>0`, or `a^x< a`. We can take the natural logarithm of both sides to get `xln(a)< ln(a)`.

Since `a>1`, `ln(a)>0`. We can divide both sides by `ln(a)` without worrying about flipping the inequality sign or dividing by `0`. Therefore, `xln(a)< ln(a)` becomes `x<1`.

Thus, the domain is `-oo< x<1`.