Question

Part A: If (62)* = 1, what is the value of x? Explain your answer. (5 points) Part B: If (6)X = 1, what are the possible values of x? Explain your answer. (5 points)

Answer 1

You have the following equation:

(6²)ˣ = 1

In order to determine what is the possible value of x, you consider the following expression:

a⁰ = 1

which means that any number exponentiated to zero equals to 1.

Then, in the given equation (6²)ˣ = 1, you can conclude that x must be equal to zero because it is the only way that the equation has a valid solution. In fact:

(6²)⁰ = 1

Hence, x = 0

In the second case, that is, for (6⁰)ˣ = 1, you take into account that the exponent must be multiplied. Thus, you have 6⁰ˣ = 1. Any number multiplied by 0 equals 0. Then, the solution for this equation are all real numbers.

x = (-∞ , ∞)