$\huge 3^x - 2^{y+2}=49 $
$\huge 2^y - 3^{x-2}+1=0 $
solve the system of equations.

Question

$\huge 3^x - 2^{y+2}=49 $
$\huge 2^y - 3^{x-2}+1=0 $
solve the system of equations.

sasogeek · Answer

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

asnaseer · Answer

try using a subtle substitution

sasogeek · Answer

how?

asnaseer · Answer

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

asnaseer · Answer

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

sasogeek · Answer

ohhh, ok :) yeah...

asnaseer · Answer

:)

turingtest · Answer

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

sasogeek · Answer

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

asnaseer · Answer

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

anonymous · Answer

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

sasogeek · Answer

lol

asnaseer · Answer

he he :D

sasogeek · Answer

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

asnaseer · Answer

hmmm - I actually get integer solutions

asnaseer · Answer

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:$$2^y=8\implies y=3$$$$3^x=81\implies x=4$$