 Hello and welcome to the session. In this session we discussed the following question which says prove that log of 288 to the base 10 is equal to 5 log 2 to the base 10 plus 2 log 3 to the base 10. Before we move on to the solution, let's discuss some laws of logarithm in which we have log of m multiplied by n to the base a is equal to log of m to the base a plus log of n to the base a. Also, log of m to the power n to the base a is equal to n into log m to the base a. This is the key idea that we use for this question. Let's proceed with the solution now. We need to prove that log of 288 to the base 10 is equal to 5 log 2 to the base 10 plus 2 log 3 to the base 10. Let us first consider the LHS which is log of 288 to the base 10. On factorizing 288 we get 288 is equal to 2 to the power 5 multiplied by 3 square. We can write this as log of 2 to the power 5 multiplied by 3 square to the base 10. Using this law, we have log of m multiplied by n to the base a is equal to log of m to the base a plus log of n to the base a. So we get this is equal to log of 2 to the power 5 base 10 plus log of 3 square to the base 10. Now using this law, log of m to the power n to the base a is equal to n multiplied by log of m to the base a. We get this is equal to 5 log 2 to the base 10 plus 2 log 3 to the base 10 which is equal to the RHS. That is we have LHS is equal to the RHS or you can say that log of 288 to the base 10 is equal to 5 log 2 to the base 10 plus 2 log 3 to the base 10. Thus hence proved this complete C session hope you have understood the solution of this question.