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hello everyone in this video weamp;#39;re going to be solving an interesting logarithmic equation first of all letamp;#39;s ask this question is this equation possible letamp;#39;s find out so we have log of x plus y equals log of x minus log of y as you know we do have the product rule and the quotient rule but we donamp;#39;t have a rule for sums but what weamp;#39;re going to do is weamp;#39;re going to be applying that rule kind of backwards and see how we can find solutions from here so i have log of x plus y is equal to the right hand side now as you know the right hand side can be written as a quotient but first of all letamp;#39;s talk about the domain of this function obviously we want this function to be well defined so x plus y needs to be greater than zero we want x to be greater than zero and we want y to be greater than zero obviously when x and y are both positive their sum is also going to be positive so these two conditions will definitely imply the third one so