 Hello and welcome to the session. In this session we discuss the following question which says express 2 upon 3 log x plus 3 upon 2 log y minus 5 log z as a single logarithm. Before we move on to the solution, let's discuss the laws of logarithms to be used in this question. First we have 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 law is log of x1 upon x2 to the base a is equal to log x1 to the base a minus log x2 to the base a. Then next law is log of x1 to the power n to the base a is equal to n into log x1 to the base a. And here this a is a positive number which is not equal to 1 then x1 x2 are also positive numbers and this n is a real number. That is n belongs to the set of real numbers. The key idea that we use for this question. Now we move on to the solution 3 log x plus 3 upon 2 log y minus 5 log z as a single logarithm. Now we will use this third law which is log 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 is equal to log upon 3 plus log of y to the power 3 upon 2 minus log of z to the power sum of the logs. So for this first law which 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. Using this law we get this is equal to log of upon 3 into y to the power 3 upon 2 minus log of z to the power. So we get difference of two logs. We can use the second law which is log of x1 upon x2 to the base a is equal to log x1 to the base a minus log x2 to the base. So using this law we get this is equal to log of x to the power 2 upon 3 into y to the power 3 upon 2 and this upon z to the power 5. Now this is a single logarithm. So upon 3 log x log y minus log z is equal to log of upon 3 into y to the power 3 upon 2 upon z to the power. Hope you understood the solution of this question.