## sasogeek Group Title $$\huge 3^x - 2^{y+2}=49$$ $$\huge 2^y - 3^{x-2}+1=0$$ solve the system of equations. 2 years ago 2 years ago

1. sasogeek

i tried using logs but i got to a dead end... :/

2. asnaseer

try using a subtle substitution

3. sasogeek

how?

4. asnaseer

$a=3^x$$b=2^y$

5. asnaseer

remember that $$2^{y+2}=2^2\times2^y=4\times2^y$$

6. sasogeek

ohhh, ok :) yeah...

7. asnaseer

:)

8. TuringTest

This is why I love this site, I never would have known what to do there...

9. sasogeek

i know right, i'm helping a friend out but i'm stuck myself so thanks to you guys ;)

10. asnaseer

I agree - I have learnt SO MUCH from this site - it is truly amazing.

11. JakeV8

where's the button for "round of applause"?

12. sasogeek

lol

13. asnaseer

he he :D

14. sasogeek

thanks guys, we did it! xD $$\large x \approx 4.069$$ and $$\large y \approx 3.263$$ can someone confirm this please... :)

15. asnaseer

hmmm - I actually get integer solutions

16. asnaseer

Using the substitutions I listed above, I get:$a-4b=49\tag{1}$$b-\frac{a}{9}+1=0\tag{2}$Multiplying (2) by 9 and moving the constant to the right-hand-side, we get:$9b-a=-9\tag{3}$Adding (1) and (3) gives:$5b=40\implies b=8$Substituting this into (1) gives:$a=81$Therefore:$2^y=8\implies y=3$$3^x=81\implies x=4$