 Hello all and welcome to this session. Today the question is if x is equal to log 1 over 5, y is equal to log 2 over 5 and z is equal to 2 log root 2 then find the value of x minus y plus z. Now before starting the question we all should know about some laws of logarithms where the first one is log m into n to the base a is equal to log m to the base a plus log n to the base a and the second one is log m over n to the base a is equal to log m to the base a minus log n to the base a and the third one is log n to the base a is equal to n log m to the base a. Now these formulas of logarithms will work out as a key idea for solving out this question and now we will start with the solution. In the question it is given x is equal to log 1 over 5, y is equal to log 2 over 5 and z is equal to 2 log root 2 and we have to find the value of x minus y plus z. Now putting the values of x, y and z there we get x minus y plus z is equal to log 1 over 5 minus log 2 over 5 plus 2 log root 2. Now for solving this we will be using the second formula which is given in the key idea and that is log m over n to the base a is equal to log m to the base a minus log m to the base a. So this will be equal to log 1 over 5 divided by 2 over 5 plus here for this we will be using the third law which is given in the key idea and that is log m over n to the base a is equal to n log m to the base a. So by using that law it will become log root 2 square. Now on solving this will become log 1 over 2 plus log root 2 square will become log 2. Now for solving this we will be using the first law which is given in the key idea and that is log m into n to the base a is equal to log n to the base a plus log n to the base a. Therefore this will become log 1 over 2 into 2. Now this will become equal to log here 2 into will be cancelled so it will be log 1. Now this will be equal to 0 because the value of log 1 is equal to 0. Hence the value of x minus y plus z is equal to 0. This is the solution for this question. That's all for the session. Hope you all have enjoyed the session.