The values of x, y, and z satisfy 2 to the x equals 3, 2 to the y equals 7, and 6 to the z equals 7. Which of the following gives the relationship between x, y, and z? We can use power laws and the given relations to solve this question. First, we know that 7 equals 6 to the z, and we can rewrite 6 as 2 times 3. Then, we expand the 2 to the 3 to the z into 2 to the z times 3 to the z. Because we know that 3 is 2 to the x, we can rewrite this purely in terms of 2 to the z times 1 plus x. We also know that 2 to the y equals 7. Therefore, 2 to the z, 1 plus x equals 2 to the y, and we know y equals z times 1 plus x. And therefore, z equals y over 1 plus x.

power laws

exponential equations

variable relationships

mathematical expressions

algebraic manipulation