 Hello and welcome to the session. In this session we discuss the following question which says if log of x plus value upon 3 is equal to half into log x plus log y show that value upon x plus x upon y is equal to 7. Before we move on to the solution, let's discuss the log of your algorithm in which we have first is log of x1 x2 to the base a is equal to log x1 to the base a plus log x2 to the base a. Then second we have log of x1 to the power n this to the base a is equal to n into log x1 to the base a positive number such that a is not equal to 1 then x1 and x2 are also positive numbers and this n is a real number that is n belongs to. Here is the key idea that we use for this question. Let's move on to the solution now. We are given that log of x plus y upon 3 is equal to half into log x log y and we are supposed to show that y upon x upon y is equal to sub log of x plus y upon 3 is equal to half into log y the first log of the algorithm stated in the key idea in which we have log x1 x2 to the base a is equal to log x1 to the base a plus log x2 to the base a. So using this log we can rewrite this expression of the right hand side so we get log of x plus y upon 3 is equal to half of log xy. Now further let's rewrite this right hand side using this log algorithm in which we have log of x1 to the power n to the base a is equal to n into log x1 to the base a. So using this log we get this would be log of x plus y upon 3 is equal to log of xy to the power 1 upon 2 and here we have log of x plus y upon 3 is equal to log of square root xy and from here we have x plus y upon 3 is equal to square root of xy. Now next we get plus y upon 3 the whole square is equal to xy. By styling this left hand side we get x square plus y square plus 2 xy and this 1 upon 9 is equal to xy. So there we have x square plus y square plus 2 xy is equal to 9 xy and from here we have x square plus y square is equal to 9 xy minus this gives us x square plus y square is equal to 7 xy. Now next dividing xy plus y square upon xy is equal to 7 xy upon xy. From here we have x is equal to this is what we were supposed to prove that is y upon x plus x upon y is equal to 7. This completes the question hope you understood the solution of this question.