SOLUTION: If {{{y=2^x}}} express the following in terms of y: a) {{{2^(2x+1)}}} b) {{{2^(1-x)}}} I tried doing it a few ways, could exactly figure out what the questions want. The ans

Algebra ->  Square-cubic-other-roots -> SOLUTION: If {{{y=2^x}}} express the following in terms of y: a) {{{2^(2x+1)}}} b) {{{2^(1-x)}}} I tried doing it a few ways, could exactly figure out what the questions want. The ans      Log On


   



Question 893221: If y=2%5Ex
express the following in terms of y:
a) 2%5E%282x%2B1%29
b) 2%5E%281-x%29
I tried doing it a few ways, could exactly figure out what the questions want.
The answers are:
a) 2y%5E2
b) 2%2Fy

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Working through....

Trying just (a).
If y=2%5Ex, then 2%5E%282x%2B1%29=2%5E%282x%29%2A2
%282%5Ex%29%282%5Ex%29%2A2
%28y%29%28y%29%2A2
2yy
2y%5E2

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

If y=2%5Ex
express the following in terms of y:
a) 2%5E%282x%2B1%29
b) 2%5E%281-x%29
I tried doing it a few ways, could exactly figure out what the questions want.
The answers are:
a) 2y%5E2
b) 2%2Fy

2%5E%282x%2B1%29______2%5E%282x%29+%2A+2%5E1______2%5Ex+%2A+2%5Ex+%2A+2%5E1
Since y+=+2%5Ex, then 2%5Ex+%2A+2%5Ex+%2A+2%5E1 becomes: y * y * 2, or highlight_green%282y%5E2%29
2%5E%281+-+x%29____2%5E1+%2A+2%5E%28-+x%29____2%5E1+%2A+%282%5E%28-1%29%29%5Ex____2+%2A+%281%2F2%29%5Ex____2+%2A+%281%2F2%5Ex%29____2%2F2%5Ex
Since y+=+2%5Ex, then 2%2F2%5Ex becomes: highlight_green%282%2Fy%29