Question

Part A: If (7exponent2)exponentX = 1, what is the value of X? Explain your answer.

Part B: If (7exponent0)exponentX = 1, what are the possible values of x? Explain your answer.

Answer 1

Answers:
Part A: The value of x must be 0
Part B: The value of x can be any real number

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Step-by-step explanation:

Part A) We have the equation (7^2)^x = 1 which simplifies to 7^(2x) = 1. The only way to get the left side equal to the right side is to have the exponent of 2x equal zero. If 2x = 0, then x = 0. So that's why x = 0 is the only solution here.

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Part B) Similar to part A above, but the exponent is slightly different now. We have (7^0)^x = 1 which turns into 7^(0*x) = 1. The exponent 0*x is really 0 no matter what x is. We can plug in any real number we want for x and the left side will always be 1. This is why the solution set to this equation is the set of all real numbers.