SOLUTION: Solve the equation. cuberoot2^(2-x) = 2^(x^2) This problem is very confusing for me, please help!

Question 61958This question is from textbook
: Solve the equation.
cuberoot2^(2-x) = 2^(x^2)
This problem is very confusing for me, please help! This question is from textbook

Found 2 solutions by stanbon, funmath:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
cuberoot2^(2-x) = 2^(x^2)
---------
Raise both sides to the 3rd power to get:
2^(2-x)=2^(3x^2)
The exponents must be equal so:
2-x=3x^2
3x^2+x-2=0
(3x-2)(x+1)=0
x=2/3 or x=-1
Cheers,
Stan H.
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
Solve the equation.
cuberoot2^(2-x) = 2^(x^2)

Since the bases are the same, their exponents are equal.

Factor by what ever method you use, I'm using arch,ac,or grouping.

Set each parntheses=0.
x+1=0 and 3x-2=0
x+1-1=0-1 and 3x-2+2=0+2
x=-1 and 3x=2
x=-1 and 3x/3=2/3
x=-1 and x=2/3
:
Check:
for x=-1
cubedroot
cubed root
cubed root
x=-1 is valid
for x=2/3
cubed root
cubed root
cubed root
x=2/3 is also valid.
There's another method for solving this, but you have to use a calculator if you take the log of both sides, so don't freak out if this is not the method you were taught.
Happy Calculating!!!
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