 Hello and welcome to the session. In this session, we discussed the following question that says, solve log x to the base 2 plus log x to the base 4 plus log x to the base 16 equal to 21 upon 4. Before we move on to the solution, let's discuss some results to be used in the solution. First, we have a law of logarithm according to which we have log x1 to the power n to the base a is equal to n into log x1 to the base a. Where this x1 is some positive number, a is also a positive number such that it is not equal to 1 and this n belongs to r that is the set of real numbers. Then we have the change of base formula according to which log n to the base a is equal to log n to the base b into log b to the base a. This is the key idea that we use for this question. Let's proceed to the solution now. We have given the equation log x to the base 2 plus log x to the base 4 plus log x to the base 16 is equal to 21 upon 4 and we are supposed to solve this equation. With this equation, we equation 1. Now, next we have we know the change of base formula which is log n to the base a is equal to log n to the base b into log b to the base a in this looking log a to the base a is equal to log a to the base b into log b to the base a. Now, this means that 1 is equal to log a to the base b into log b to the base a since we know the log of a to the base a is equal to 1. So, this means we have log a to the base b is equal to 1 upon log b to the base a. Let this be the result. Now, next using this result to in equation 1 we get log x to the base 2 could be now written as 1 upon log 2 to the base x plus log x to the base 4 can be now written as 1 upon log 4 to the base x plus log x to the base 16 can be written as 1 upon log 16 to the base x and this is equal to 21 upon 4. So, further we have 1 upon log 2 to the base x plus 1 upon log 2 square that is we can write 4 as 2 square to the base x plus 1 upon log 2 raise to the power 4 that is we have written 16 as 2 raise to the power 4 and this to the base x is equal to 21 upon 4. Now, for these two denominators this law of logarithm stated in the key idea which is log x1 to the power n to the base a is equal to n into log x1 to the base a. So, using this law we can rewrite the denominators of these two terms 1 upon log 2 to the base x plus 1 upon 2 into log 2 to the base x plus 1 upon 2 to the base x this is equal to 21 upon 4. Now, taking 1 upon to the base x where we have 1 upon log 2 to the base x into 1 plus 1 upon 2 plus 1 upon 4 equal to 21 upon 4. This gives us 1 upon log 2 to the base x and we take the lcm here which is 4 so here we have 4 plus 2 plus 1 and this one is equal to 21 upon 1 upon log 2 to the base n upon 4 is equal to take this means we have 1 upon log 2 to the base x equal to 21 upon 4 into 1 upon 7. This 4 4 cancels and 7 3 times is 21 that is 1 upon log 2 to the base x is equal to 3 for result 2 we have log a to the base b is equal to 1 upon log b to the base a. So, using this result in the LHS we have log x to the base 2 is equal to that log of x to the base a equal to n means that x is equal to a to the path n. Therefore, using this in this we get f is equal to 2 raise to the path that we have solved the equation to get the value of fx equal to 8 is our final answer. This completes the session so we have understood the solution of this question.