SOLUTION: The original problem was (4^(x+y))/(8^(x+y))=512; I simplified to (1/2)^(x+y)=512, then multiplied by 2 and got 1^(x+y)=1024, but i dont know how to get that into the form x=.... o

Algebra ->  Exponents -> SOLUTION: The original problem was (4^(x+y))/(8^(x+y))=512; I simplified to (1/2)^(x+y)=512, then multiplied by 2 and got 1^(x+y)=1024, but i dont know how to get that into the form x=.... o      Log On


   

Question 608471: The original problem was (4^(x+y))/(8^(x+y))=512; I simplified to (1/2)^(x+y)=512, then multiplied by 2 and got 1^(x+y)=1024, but i dont know how to get that into the form x=.... or y=....
Please Help!!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First of, a general principle in Math is that you need as many equations as you have variables. Since you have two variables but only one equation, we will not be able to find the value of each equation. But we can transform the given equation into a simpler, more useful form.

%284%5E%28x%2By%29%29%2F%288%5E%28x%2By%29%29=512
%284%2F8%29%5E%28x%2By%29=512
%281%2F2%29%5E%28x%2By%29=512
Nothing wrong so far. But if you multiply both sides by 2:
2%2A%28%281%2F2%29%5E%28x%2By%29%29=2%2A%28512%29
you do NOT get
1%5E%28x%2By%29+=+1024
because the order of operations (aka PEMDAS) requires that we raise 1/2 to the x+y power before we do any multiplying. So we're still at:
%281%2F2%29%5E%28x%2By%29=512
When working with exponential equation like this, you learn that if you can express both sides of the equation as powers of the same number, then you can simplify them in a relatively easy way. The "trick" with this equation is to figure out that 1/2 and 512 are both powers of 2! 2%5E%28-1%29+=+1%2F2 and 2%5E9+=+512. You should know the first one. The second one you probably would have to find using trial and error. Replacing 1/2 and 512 with these powers of 2 we get:
%282%5E%28-1%29%29%5E%28x%2By%29=2%5E9
On the left side, since it is a power of a power, the rule is to multiply the exponents:
2%5E%28-x-y%29=2%5E9
The equation now says that two powers of 2 are equal. The only way this can happen is if the two exponents are equal. So:
-x-y=9
This equation is good. But some prefer fewer minus signs. Multiplying each side by -1 we get:
x%2By+=+-9

Without another equation, this is as far as we can go.