The function is .

Differentiate on each side with respect to .

Derivative of a logarithmic function : .

Logarithm of a negative value is undefined.

Case 1: If both the terrms are positive then .

 and 

 and .

The condition is true for .

Domain is .

Case 2: If both the terrms are negative  then .

 and 

 and 

The condition is true for .

Domain is 

Therefore the domain of the function is .

.

The domain of the function is .