 Hello and welcome to the session. In this session we discuss the following question which says, if 2 to the power 3x minus 1 plus 10 divided by 7 is equal to 6 then find x. Let's move on to the solution. We are given that 2 to the power 3x minus 1 plus 10 when divided by 7 gives us 6 and we need to find the value for x. Consider 2 to the power 3x minus 1 plus 10 upon 7 is equal to 6. This gives us 2 to the power 3x minus 1 plus 10 is equal to 7 into 6. That is we get 2 to the power 3x minus 1 plus 10 is equal to 42. This further implies 2 to the power 3x minus 1 is equal to 42 minus 10. This further implies 2 to the power 3x minus 1 is equal to 32. Now let's factorize 32. 2 16 times is 32. 2 8 times is 16. 2 4 times is 8. 2 2 times is 4. 2 1 times is 2. So we say that 32 is equal to 2 multiplied to itself 5 times that is 32 is equal to 2 to the power 5. That is we get 2 to the power 3x minus 1 is equal to 2 to the power 5. As you can see the base is the same for the right side and the left side that is the base is 2. Now we compare these exponents we get 3x minus 1 is equal to 5. This means that 3x is equal to 5 plus 1 that is 3x is equal to 6. Now dividing both sides by 3 we get x is equal to 2. So our final answer is x equal to 2. So this completes the session. Hope you have understood the solution for this question.