Can someone help me out with this question about logs? please

Question

$$3^{2x}-2^{2y}=17$$ Find $x+y$.

Here is what I did so far: Let $m=3^{2x}$ and let $n=2^{2y}$

$x=\frac{\log_3m}{2}$ , $y=\frac{\log_2n}2$

$$x+y= \frac{\log_3m+\log_2n}{2} $$

x+y= (base(3)17+n)+(base(2)n)/2

don't know what to do from there

I think you want to assume that $x,y$ are natural numbers, no? — lulu, Mar 06 '16 at 13:19

score 3 · Accepted Answer · answered Mar 06 '16 at 13:15

3

$$17=3^{2x}-2^{2y}=(3^x-2^y)(3^x+2^y)$$

and now remember $\;17\;$ is prime. I don't think logarithms are required here.

answered Mar 06 '16 at 13:15

DonAntonio

How do you know that $x,y \in \mathbb{Z}$? – gt6989b Mar 06 '16 at 13:17
@gt6989b Thank you. I don't, I just assumed as it looked straighforward. But, of course, I could be wrong. Hopefully the asked will explain. – DonAntonio Mar 06 '16 at 13:20
1

yes it does state x,y∈ℤ. I just forgot to include it. Thank you very much – Philip O'Neill Mar 06 '16 at 13:23

1 Answers1