 Hello and welcome to this session. In this session we will discuss a question which says that find the solution of the given system of equations. And the equations are y is equal to log x plus 1 to the base 2 and y is equal to 5 minus log x minus 3 to the base 2. Now let us start with the solution of the given question. Now we have given this system of equations. Now let this be equation number 1 and this be equation number 2. Now this is of the form y is equal to f of x and y is equal to g of x. Now the solution of this system of equations will be given by the equation f of x is equal to g of x. Now this is f of x and this is g of x. So this is the solution of the system of equations is given by f of x is equal to g of x. So we have log x plus 1 to the base 2 is equal to 5 minus log x minus 3 to the base 2. Now we need log terms together. This implies log x plus 1 to the base 2 plus log x minus 3 to the base 2 is equal to 5. Now by using the property of log ribbons we know that log n to the base b plus log n to the base b is equal to log nn to the base b. So using this property we have log 1 the whole into x minus 3 the whole and this complete whole to the base 2 is equal to 5. Now by definition of log we have y is equal to log x to the base b. If the log is x is equal to b raise to power y x plus 1 the whole into x minus 3 the whole is equal to 2 raise to power 5. And this implies x square plus x minus 3 x minus 3 is equal to 2 raise to power 5. Now this implies x square plus x minus 3 x is minus 2 x minus 3 is equal to 2 raise to power 5 is 32 which further implies x square minus 2 x minus 3 minus 32 is equal to 0. And this gives x square minus 2 x minus 35 is equal to 0. Now this is the analytic equation in x so we will solve this by definition. Now by definition of log n term this implies x square minus 7 x plus 5 x minus 35 is equal to 0. Now this implies now from these 2 terms taking x common it will be x into x minus 7 the whole and from these 2 terms taking 5 common it will be plus 5 into x minus 7 the whole is equal to 0. This implies x y is 7 the whole into x plus 5 the whole is equal to 0 which implies x is equal to 7 and x is equal to minus 5. Now for x is equal to minus 5 the values of y in both the functions is not defined because log of negative numbers does not exist so we will start x is equal to minus 5. Now we are left with only x is equal to 7. Now let us find corresponding values of y for x is equal to 7. First of all let us put x is equal to 7 in equation 1. So we have y is equal to log 7 plus 1 to the base this implies y is equal to log 8 to the base 2. Now again by using definition of log we have 2 raise to power y is equal to 8 this implies 2 raise to power y is equal to now 8 can be written as 2 raise to power 3. So this implies y is equal to 3 because this is same so we can equal the parts therefore for x is equal to 7 we get y is equal to 3 the solution of the given system of equations is order pair 3 7 and this completes our session hope you all have enjoyed the session. .