SOLUTION: NOTE: when I previewed the question it seemed like the fractional exponents got cut off at the top. In case they can't be seen, the first three are (2/7) and the last two are (7/2)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: NOTE: when I previewed the question it seemed like the fractional exponents got cut off at the top. In case they can't be seen, the first three are (2/7) and the last two are (7/2)      Log On


   

Question 845665: NOTE: when I previewed the question it seemed like the fractional exponents got cut off at the top. In case they can't be seen, the first three are (2/7) and the last two are (7/2).
My teacher wrote her own series of homework problems with the only instructions being "use the One-to-One Property." I tried to find an answer by manipulating the equations (isolating the term being raised to the 'x' power on one side of the equal sign), but I have not been able to find a common base to finish solving the problems.
x%5E%282%2F7%29-12=5
I simplified the problem to x%5E%282%2F7%29=17
I then proceeded to solve it as follows, but this method did not seem to be One-to-One:
x%5E%28%282%2F7%29%2A%287%2F2%29%29=17%5E%287%2F2%29

x=%28sqrt%2817%29%29%5E7
Any help is greatly appreciated. Thank you!

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Your work is good, because it makes sense. What is the "one-to-one" property that you are supposed to use? The steps you used to solve for x are already correct.