# Homework Help: Tricky exponential question

1. Sep 17, 2009

### yoleven

1. The problem statement, all variables and given/known data
for x and y satisfying x-y=2 and 2$$^{x}$$-2$$^{y}$$=6
find 2$$^{x}$$+2$$^{y}$$.

3. The attempt at a solution
x-y=2 ; x=2+y
log$$_{2}$$ 2$$^{x}$$-log$$_{2}$$2$$^{y}$$=log$$_{2}$$6

log 6/log2=2.585

x-y=2.585 but this violates the intitial condition x-y=2

where am i going wrong?

2. Sep 17, 2009

### nietzsche

I don't think you need to use logs.

x-y=2
x=y+2

2^(y+2) - 2^y = 6

I think you should be able to figure it out from that.

3. Sep 17, 2009

### Bohrok

Yes, use substitution. Also
log2(a + b) $\neq$ log2a + log2b

4. Sep 17, 2009

### yoleven

I'm not seeing what to do. I see the substitution but then I don't know what to do.

5. Sep 18, 2009

### nietzsche

Let's take
x - y = 2
x = y + 2

substitute into your equation

2y+2 - 2y = 6
(2y)(22) - 2y = 6
2y(4-1) = 6
...

You don't even have to solve for x and y explicitly.

6. Sep 18, 2009

### yoleven

thank you very much.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook