 Hello and welcome to the session. In this session we discussed the following question which says, find the logarithm of 0.125 to the base 2. Now we know that if we are given log of the number n to the base a is equal to x, this means a to the power of x is equal to n. This is the key idea that we use for this question. Let's proceed with the solution now. We need to find the logarithm of 0.125 to the base 2. We suppose let log of 0.125 to the base 2 be equal to x. Now using the key idea we get that this implies 2 to the power of x is equal to 0.125. Let us now simplify 0.125 that is this could be written as 125 upon 1000, 25 5 times is 125 and 25 40 times is 1000 and 5 8 times is 40 so this is equal to 1 upon 8 that is we have 2 to the power of x is equal to 1 upon 8 or we can write this as 2 to the power x is equal to 1 upon 2 to the power 3 since 2 cube is 8 further we can say 2 to the power x is equal to 2 to the power minus 3. So from this we conclude that x is equal to minus 3 and we had assumed x to be the logarithm of 0.125 to the base 2. Thus we can say that log of 0.125 to the base 2 is equal to minus 3. This is our final answer. This completes the session. Hope you have understood the solution of this question.