 Hello and welcome to the session. In this session we will discuss the question which says that considering the two functions y is equal to x square and y is equal to 2 raised to the power x estimate the solution of the equation 2 raised to the power x is equal to x square as accurately as possible. Now let us start with the solution of the given question. Now when we are given the system of equations y is equal to x square and y is equal to 2 raised to the power x and we have to estimate the solution of the equation 2 raised to the power x is equal to x square as accurately as possible. It means we have to find the point of intersection of the given equations. Now we will obtain its solution by making table of values and drawing the graph of two equations. First of all let us take the equation y is equal to x square. Now it is an upright facing parabola with y axis as the axis of symmetry. Now let us make its table of values. First of all let us put x is equal to 0 in this equation. Now for x is equal to 0, y is equal to 0. Then for x is equal to 1, y is equal to 1 square that is 1. Then for x is equal to 2, y is equal to 2 square that is 4. Now for x is equal to 3, y is equal to 3 square that is 9. And for x is equal to 4, y is equal to 4 square that is 16. Similarly for x is equal to 5, y is equal to 25 and for x is equal to 6, y is equal to 36. Now let us plot all these points on the coordinate plane that is we have to draw this upright facing parabola keeping in mind the y axis as the axis of symmetry. First of all let us plot the point 0, 0 on the graph. So this is the point 0, 0. Then the next point has coordinates 1, 1. So this is the point with coordinates 1, 1. So we have drawn this upright facing parabola by plotting all the points. Keeping in mind the y axis as the axis of symmetry is the required graph of the equation y is equal to x square. Now let us take the second equation that is y is equal to 2 raise to power x. Now this is an exponential function. Now let us make its table of values. Now for x is equal to minus 1, y is equal to 2 raise to power minus 1 that is equal to 1 upon 2 which is equal to 0.5. So for x is equal to minus 1, y is equal to 0.5. Then for x is equal to 0, y is equal to 3 raise to power 0 that is 1. Then for x is equal to 1, y is equal to 2 raise to power L that is equal to 2. For x is equal to 2, y is equal to 2 raise to power 2 that is 4. For x is equal to 3, y is equal to 2 raise to power 3 that is 8. for x is equal to 4, y is equal to 2 raised to power 4 that is equal to 16, then for x is equal to 5, y is equal to 2 raised to power 5 that is equal to 32. Now let us plot all these points on the graph. Now this is the point with coordinates minus 1, 0.5 then this is the point with coordinates 0, 1. Similarly we will plot all these points on the graph to obtain the curve of the exponential function y is equal to 2 raised to power x. So by plotting all these points and then joining the points we get the graph that is this green curve of the exponential function y is equal to x. Now in this graph you can see that the two curves intersect each other at three points. This is the first point, this is the second point and this is the third point. Let us denote these points by a, b and c. Now at point a we can observe that the x coordinate is approximately minus 0.7, y coordinate is approximately 0.8, so point a has coordinates minus 0.7, 0.8. Then here you can see point b has coordinates, 2, 4, t has coordinates, 4 is 16. So these three will give the solution of the given system of equations thus solution set of equation is to power x is equal to x square is the set containing the order pairs minus 0.7, 0.8, then the order pair 2, the order pair 4, 6, 9. So this is the required answer and this completes our session. Hope you all have enjoyed the session.