 Hello and welcome to the session. In this session we discuss the following question which says find x, so that 2 upon 5 to the power 4 multiplied by 2 upon 5 to the power minus 5 is equal to 2 upon 5 to the power x minus 1. Now if we are given a rational number a upon b and m and n are the positive integers then a upon b to the power m multiplied by a upon b to the power n is equal to a upon b to the power m plus n. This is the key idea for this question. Let's move on to the solution now. We are given that 2 upon 5 to the power 4 multiplied by 2 upon 5 to the power minus 5 is equal to 2 upon 5 to the power x minus 1. We need to find the value for x. Now using the key idea which says that for any rational number a upon b and positive integers m and n a upon b to the power m multiplied by a upon b to the power n is equal to a upon b to the power m plus n. So applying this on the left hand side of this expression we get 2 upon 5 to the power 4 minus 5 and this is equal to 2 upon 5 to the power x minus 1. Or this further gives us 2 upon 5 to the power minus 1 is equal to 2 upon 5 to the power x minus 1. Now equating the powers of the rational number 2 upon 5 on both the sides we get minus 1 is equal to x minus 1. This means that x is equal to minus 1 plus 1 or you can say we get x is equal to 0. So our final answer is x equal to 0. This completes the session. Hope you have understood the solution for this question.