 Hello and welcome to the session. In this session, we discussed the following question that says given log x to the base 10 equal to a and log y to the base 10 equal to b write down 10 to the power 2b in terms of y and if log p to the base 10 is equal to 2a minus b expressed p in terms of x and y. Let us first discuss some laws of logarithms to be used in this question. First we have log of m upon n to the base a equal to log m to the base a minus log n to the base a then log of m to the power n to the base a is equal to n into log m to the base a. This is the key idea that we use for this question. Let us proceed with the solution now. We are given log x to the base 10 is equal to a and log y to the base 10 is equal to b. So this means 10 to the power a is equal to x and 10 to the power b is equal to y. We now need to express 10 to the power 2b in terms of y, 10 to the power 2b could be written as 10 to the power b whole square. Now we know that 10 to the power b is equal to y so this is equal to y square that is we have 10 to the power 2b is equal to y square. So this is the answer for the first part of the question. Now let us move on to the second part of the question in which we are given log p to the base 10 is equal to 2a minus p. We need to express p in terms of x and y. First of all we substitute the values of a and b here. We know that a is equal to log x to the base 10. So this is equal to 2 into log x to the base 10 minus p which is equal to log y to the base 10. This law for this expression we get log x square to the base 10 minus log y to the base 10. Now on the right hand side we have difference of two logarithms. So we would use this law. So using this law here we get log p to the base 10 is equal to log of x square upon y to the base 10. This gives us p is equal to x square upon y. Thus our answer for the second part of the question is p equal to x square upon y. So this completes the solution. Hope you have understood the solution of this question.