 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that solve for y and the equation given is y is equal to log of square root of 125 to the base 5. We know that the relationship between logarithmic and exponential form is given by y is equal to log of x to the base b and this is equivalent to b raised to the power y is equal to x where this is the logarithmic form of the equation and this is the exponential form of the equation. With this key idea let us proceed to the solution. Here we have y is equal to log of square root of 125 to the base 5. From the key idea we know that the logarithmic form of the equation can also be written in the exponential form of the equation and vice versa. This is the logarithmic form of the equation and using this key idea we can transform this logarithmic form of the equation into exponential form and it can be written as 5 raised to the power y is equal to square root of 125. We can also write this equation as 5 raised to the power y is equal to 125 raised to the power 1 upon 2. Now writing 125 in parts of 5 we get 5 raised to the power y is equal to 5 raised to the power 3 whole raised to the power 1 upon 2. Now simplifying this exponent we get 5 raised to the power y is equal to 5 raised to the power 3 into 1 by 2 that is 3 by 2. Since base is same so we can equate the parts. Here we can see that we have same base 5 so we can equate the parts and we get y is equal to 3 by 2. Hence we get the value of y as 3 by 2 which is the required answer. This completes our session. Hope you enjoyed this session.