 In this session we discussed the following question which says prove that x to the power of log y minus log y into y to the power of log z minus log x into z to the power of log x minus log y is equal to 1. 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 x to the base a is equal to log x1 to the base a plus log x1 to the base a then next law is log of 1 to the power m to the base a is equal to m into log x1 to the base m x2 are positive numbers then a is also positive number such that a is not equal to 1 and this m is a real number that is m belongs to the set of real numbers. This is the key idea that we use for this question. Let us move on to the solution we are supposed to prove log y minus log z into y to the power of log z minus log x into z to the power of log x minus log y is equal to 1. Before we suppose let p be equal to x to the power of log y minus log z into y to the power of log z into z to the power of log x minus log y. Now next we have taken log p is equal to log of log y minus log z into y to the power log z minus log x into z to the power log x minus log y. Now this right hand side is the log of the product of the factors. So using this first law of logarithm which is log x1 x2 to the base a is equal to log x1 to the base a plus log x2 to the base log p is equal to log x to the power log y minus log z y to the power log z minus log x log of on the right hand side we would use the second law of logarithm which is log x1 to the power n to the base a is equal to n into log x1 to the base using this law we get log p is equal to log y log z and this way into log x log x and this way into log y and this way into log z is equal to log x into log y minus log z into log y log y into log by the right hand side log x into log y cancels with minus log x into log y and log y into log z cancels with minus log y into log z log x into log z cancels with minus log x into log z this means the log p is equal to and 0 is log 1 this means that p is equal to y we have supposed therefore we can say the x log y minus log z y to the power log y is equal to 1 this is what we were supposed to mention but we understood the solution of this question.