 Hello and welcome to the session. In this session we discuss the following question that says, determine the value of m if log AP1 to the base m is equal to 8. We know that if log of the number m to the base a is equal to x this means that a to the power of x is equal to the number n. This is the key idea that we use in this question. Let's proceed with the solution now. We are supposed to find the value of m and we are given that log of 81 to the base m is equal to 8. The idea we have that this means m to the power of 8 is equal to 81. Now to find the value of m we will factorize 81 and we write this as some number to the power of 8 so that we get the value of m. Factorizing 81 we get this that is 81 is equal to 3 to the power of 4 or this could be written as root 3 whole square and this whole to the power of 4 which means this is equal to root 3 whole to the power of 8 that is 81 is written as root 3 to the power of here we get m to the power of 8 is equal to root 3 whole to the power 8. Now here as the exponents are same that is 8 so this means that the value of m is equal to root 3. Therefore the value of m is equal to root 3 our final answer this complete session hope you have understood the solution of this question.