 Hello and welcome to this session. In this session we will discuss the properties of logarithms. First we have the logarithm. We have logarithm of the product of the more positive numbers to any real base is equal to the sum of the logarithms to the same base. To be positive numbers one half log of m into n to the base a is equal to log n to the base a plus log n to the base. In that we discuss logarithm of a quotient the logarithm of the quotient two positive numbers to any real base is equal to the logarithm of the numerator, the logarithm of the denominator to the same base. Is a real base given that log of m upon n to the base a is equal to log n to the base a minus log n to the base a. m equal to 1 log of 1 upon n would be equal to log 1 to the base a minus log n to the base a log of 1 upon n to the base a is equal to log 1 to the base a is 0 minus log n to the base a. Thus we have log of 1 upon n to the base a is equal to minus log n to the base a that we discuss is logarithm the logarithm of a number of index to any real base equal to the product of the index and the logarithm of the given number to the same base. Where again this n is some positive number some real base into the base a is equal to n into log n to the base in logarithms to compute 0.233 and 1 to the base using logarithms and the properties of logarithms. For this we suppose that x be equal to 0.233 into 3.12. Now we get log x is equal to log of 0.233 into 3.12. According to which we have log of m into n to the base a is equal to log n to the base a plus log n to the base a. Now using this property to the right hand side of the given expression that is we apply this property here we get log x is equal to log of 0.243 plus log of 3.12. Now property for 3 is equal to 1 by 0.12 is equal to 0.4956 plus 0.4942 log x is equal to minus 1 to 7 by 8. which means equal to 1 by 98. So this means that x is equal to, without the empty log of this number, which gives us 0.75 x is equal to 0.7582. And we are assumed to be equal to the product of 0.243 and 3.12. So we can now say 0.243 into 3.12 is equal to 0.7582. Two numbers using the property of logarithms. When we divide two numbers using the properties of logarithm, also we can find the power of any given number. This is the question that we have understood the properties of logarithms.