 Hello all and welcome to the session. Here the question is evaluate without using tables log 8 to the base 10 plus log 25 to the base 10 plus 2 log 3 to the base 10 minus log 18 to the base 10. Now before starting the solution of this question we all should know the laws of logarithms where the first law is log m into m to the base a is equal to log m to the base a plus log m to the base a. The second law is log m over m to the base a is equal to log m to the base a minus log n to the base a. And the third law is log m raised to the power n to the base a is equal to m log n to the base a. Now these laws of logarithms will work as a key idea for solving out this question. And now we will start with the solution. Here we have to evaluate log 8 to the base 10 plus log 25 to the base 10 plus 2 log 3 to the base 10 minus log 18 to the base 10. Now for this we will be using the third law which is given in the key idea and which is log m raised to power n to the base a is equal to m log n to the base a. This implies log 8 to the base 10 plus log 25 to the base 10 plus log 3 raised to power 2 to the base 10 minus log 18 to the base 10. Now for solving this we will be using the first law which is given in the key idea and that is log m over m to the base a is equal to log m to the base a plus log m to the base a. Therefore this will become log 8 into 25 into 3 raised to power 2 over the base 10 minus log 18 to the base 10. Now for solving this we will be using the second law which is given in the key idea and which is log m over n to the base a is equal to log m to the base a minus log m to the base a. Then we get log 8 into 25 into 3 square is equal to 9 over 18 over 9 to the base 10. Now here 9 out of 2 is equal to 18 and 2 into 4 is equal to 8 so this implies log 4 into 25 will become 100 to the base 10. Now this will become log 10 to the base 10 because log 100 to the base 10 is equal to log 10 raised to power 2 to the base 10 where 10 raised to power 2 is equal to 100. This implies we will be using the third law and then we will get log 10 raised to power 2 to the base 10 is equal to p log 10 to the base 10. This implies into 1 because the value of log 10 to the base 10 is equal to 1. Now this will be equal to hence the value of log 8 to the base 10 plus log 25 to the base 10 plus 2 log 3 to the base 10 minus log 18 to the base 10 is equal to 2. So this is the solution of the given question. That's all for this session. Hope you all have enjoyed the session.