 Hello and welcome to the session. Here the question is given if log2 is equal to 0.3010 and log3 is equal to 0.4771 then find the value of log80. Now before starting the solution we all should know the laws of logarithms. Now here the first law is log n into n to the base a is equal to log n to the base a plus log n to the base a. Then the second law is log n raised to power n to the base a is equal to log n to the base a minus log n to the base a. And the third law is log n raised to power n to the base a is equal to n log n to the base a. Now these two laws will work as the key idea for solving out this question. Now let us start with the solution. Now here it is given log2 is equal to 0.3010 and log3 is equal to 0.4071. We have to find the value of log80. Now log80 can be written as log2 raised to power 4 into 5 because of factorization we get the factors of 80 like this and 80 can be written as 2 raised to power 4 into 5. And now for solving this we will be using the first law of logarithm which is given in the key idea and that is log n into n to the base a is equal to log n to the base a plus log n to the base a. So this will be equal to log 2 raised to power 4 plus log 5. Now for this we will be using the third law of logarithm which is given in the key idea and that is log n raised to power n to the base a is equal to n log n to the base a. So this will be equal to third law and for log 5 sends in the question the value of log 2 and log 3 is given. So we have to express log 5 in terms of log 2 or log 3. So we will write log 5 as log 10 by 2. Now for this we will be using the second law of logarithm which is given in the key idea is log to the base a is equal to log n to the base a minus log n to the base a. So this will be equal to third law 2 and using the second law it will become plus log 10 minus log 2. This will be equal to 4 log 2 minus log 2 we give 3 log 2 plus log 10 and this is equal to log 2 plus 1 because the value of log 10 is equal to 1. Further this is equal to 3 putting the value of log 2 that is 0.3010 plus 1. This is equal to 0.9030 plus 1 which is equal to 1.9030. Hence the value of log 80 is equal to 1.9030. So this is the solution of the given question that's all for this session hope you all have enjoyed the session.