 Hello and welcome to the session. In this session, we are going to discuss the following question which says that change part A, y is equal to 3 upon 2 into 5 raised to power x into logarithmic form part B, y is equal to log of y upon 9 to the base 8 into y is equal to A into B raised to power x form. We know that the relationship between logarithmic and exponential form is given by y is equal to log of x to the base B is equivalent to B raised to power y is equal to x that is y is equal to log of x to the base B can be written as B raised to the power y is equal to x and vice versa. With this key idea let us proceed to the solution. Now in the first part we have y is equal to 3 upon 2 into 5 raised to the power x this is the exponential form and we will convert it into logarithmic form. Here the given exponential equation is of the form y is equal to A into B raised to power x. So we first write it in the form y upon A is equal to B raised to power x and then we will apply the key idea to write it in logarithmic form on comparing these two equations we see that A is equal to 3 upon 2 that is in the exponential equation y is equal to 3 by 2 into 5 raised to power x the value of A is equal to 3 upon 2. So we divide this equation by A that is 3 by 2 on both the sides. So divide both sides by 3 by 2 and we get y upon 3 by 2 is equal to 3 by 2 whole upon 3 by 2 into 5 raised to power x which implies that 2 upon 3 into y is equal to 5 raised to power x. Now from the key idea we know that the relationship between logarithmic and exponential form is given by y is equal to log of x to the base B which can also be written as B raised to the power y is equal to x. Now using this relationship we can write log of 2y upon 3 to the base 5 is equal to x that is the required equation in logarithmic form. Therefore the logarithmic form of the given equation is given by log of 2y upon 3 to the base 5 is equal to x which is the required answer to the first part of the question. Now let us start with part B of the question which says change log of y upon 9 to the base 8 is equal to x into exponential form that is in the form y is equal to a into B raised to power x. Now we see that log of y upon 9 to the base 8 is equal to x is in the form log of y upon a to the base B is equal to x and we need to convert it in exponential form that is in the form y is equal to a into B raised to power x. So again using this key idea we can write log of y upon a to the base B is equal to x as y upon a is equal to B raised to power x which further implies that y is equal to a into B raised to power x. So log of y upon 9 to the base 8 is equal to x can be written as y upon 9 is equal to 8 raised to power x. Now multiply by 9 on both sides we get 9 into y upon 9 is equal to 9 into 8 raised to power x which implies that y is equal to 9 into 8 raised to power x which is the required exponential form. This completes our session. Hope you enjoyed this session.