 Hello and welcome to the session. In this session we discussed the following question which says, simplify 2 log 9 minus log 18. Before moving on to the solution, let's discuss one law of logarithm in which we have log of m upon n to the base a, that is, logarithm of the quotient of any two positive numbers to any real base a which is greater than 1 is equal to log m to the base a minus log n to the base a, that is, logarithm of the numerator minus logarithm of the denominator to the same base a. Also, we have another property in which we have log of m to the power n to the base a is equal to n into log of m to the base a. Here also the base a is any real base greater than 1. This is the key idea that we use for this question. Let's proceed with the solution now. We need to simplify the expression 2 log 9 minus log 18. Now, using the second law of logarithm we say that 2 log 9 can be written as log of 9 to the power 2 minus log 18 or further we get log 81 minus log 18. Now, using this property, that is the first property, we find that log m to the base a minus log n to the base a is equal to log m upon n to the base a. So, this could be written as log 81 upon 18. Now, 9 2 times is 18 and 9 9 times is 81. So, this is equal to log of 9 upon 2. Thus, log 9 upon 2 is our final answer. This completes the session. Hope you have understood the solution of this question.