 Hello and welcome to the session. In this session, we discussed the following question that says, simplify 1 upon 2 log 25 minus 2 log 3 plus log 18. Before we move on to the solution, let's discuss some laws of logarithm. First, we have log of m multiplied by n to the base a is equal to log m to the base a plus log m to the base a then log m upon m to the base a is equal to log m to the base a minus log n to the base a and log m to the power n to the base a is equal to n into log of 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 simplify the expression 1 upon 2 log 25 minus 2 log 3 plus log 18. Now, using this law that is the third law here, we will simplify these two terms. So we get this is equal to log of 25 to the power of 1 upon 2 minus log of 3 square plus log 18 as it is. Now, this is equal to log of 25 is 5 square whole to the power 1 upon 2 minus log 3 square that is 9 plus log 18. This is further equal to log 5 plus log 18 minus log 9. Now, since we know that log of m multiplied by n to the base a is equal to log m to the base a plus log n to the base a. So using this law, we get this is equal to log of 18 multiplied by 5 minus log 9 that is we have log 90 minus log 9. Now, from the second law stated here, we have log of m upon n to the base a is equal to log m to the base a minus log n to the base a. So using this law, we get this is equal to log 90 upon 9. Now 9, 10 times is 90. So this is equal to log 10. Now, as we know that when the base is not indicated, it means that the base is 10. So this could also be written as log 10 to the base 10 and we know that log of a to the base a is equal to 1. So log of 10 to the base 10 is equal to 1. So finally, we have half into log 25 minus 2 log 3 plus log 18 is equal to 1. This is our final answer. This completes the session. Hope you have understood the solution of this question.