The reason of the [apparent] contradiction is that the identity is true only if ...
I show two workings to solve the equation below using the simplification rules for logs.
My textbook does not indicate how and when solutions are lost using the log simplification rules. Clearly if we use the rule negative solutions might be lost.
Where can I find more information about this I want to understand the problem better.
, divide both sides by
The first solution is wrong. The rule doesn't hold (looses solutions) for even exponents.
My previous answers has been a little 'approximated' and I apologize for that ...
If x is a real number and x<0, then is...
In this case however is
The consequence is that the general expression you have written holds for any value of b, x, and y with , and ...