Simple algebra questions:
If 2^x*4^y = 32 and 3^x/9^y =3, what are the values for x and Y?

Question

Simple algebra questions:
If 2^x*4^y = 32 and 3^x/9^y =3, what are the values for x and Y?

jim766 · Answer

for the first one

2^x * 4^y = 32        think of the ways to mult 2 numbers and get 32

                                1 * 32,  2 * 16, 4 * 8     now pick the pair that you can use

   8 * 4 = 32
2^3 * 4^1 = 32       x = 3, y = 1

make sense?

chillout · Answer

Indeed it does. But is there any other way besides trial and error?

jim766 · Answer

probably, but I don't know it  lol

anonymous · Answer

Trial and error would probably be your best bet:)

chillout · Answer

I mean, I can rewrite this as$$2^{x+2y}\ \ and\ \ 3^{x-2y}$$
But I think it would get a bit tiring from here

anonymous · Answer

Yeahh it would. The trial and error method isn't 100% accurate but it's quite close

jim766 · Answer

for the 2nd one, 9/3     what exponent can make each number its reciprocal

jim766 · Answer

^    9/3 = 3

chillout · Answer

Yes, I know, I was thinking in another method aside from this one, but thanks anyways. There will be some questions about it in a moment :)

chillout · Answer

Thanks for the help too, @Shawna.marie

anonymous · Answer

Nytime:)

irishboy123 · Answer

there is no need to guess

use your cleverly rewritten formula and also use logs.

EG:
(x+2y) ln(2) = ln32
(x-2y) ln(3) = ln3

x+2y = ln32/ln2 = 5
x-2y = 1

add them: 2x = 6: x=3, y = 1
check (3) - 2(1) = 1

and there you have it!!

anonymous · Answer

Omg that is like ninja status:)