Answer:
1. Skyler's processes are incorrect. She put (3^6)^x = 9, but when working with exponential problems, both sides have to have the same base. 3 does not equal nine, so you can automatically rule out her approach.
2. Robert's processes are correct. He set both bases equal to each other and then solved for the exponents.
3. Kaitlyn is also correct, she set the bases equal to 3 and solved for the exponents.
Step-by-step explanation:
When working with exponents, the goal is to get the bases equal to each other. In this case, you could have set it equal to 9 (which Robert did) or you could have set it equal to 3 (like Kaitlyn did). But you never want the bases to be conflicting, which is what Skyler did. Just by looking at the problem and using deductive reasoning, it is likely that Robert and Kaitlyn are both correct, since they have the same answers, although they used different methods, but it is still important to look at the steps.
Skyler's one mistake was setting 3 = 9, because that is impossible. If you plug in her answer of 3/2 into x, you get a ridiculous number of 19,683 = 9, which is not possibly true. For the others, when you plug in 1/3, you get 729^(1/3) = 9, so 9=9.
Hopefully this makes sense, if not, I can try to explain it better. Thanks much & have a wonderful day.
