ChillOut
  • ChillOut
Simple algebra questions: If 2^x*4^y = 32 and 3^x/9^y =3, what are the values for x and Y?
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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Jim766
  • Jim766
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
  • ChillOut
Indeed it does. But is there any other way besides trial and error?
Jim766
  • Jim766
probably, but I don't know it lol

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anonymous
  • anonymous
Trial and error would probably be your best bet:)
ChillOut
  • ChillOut
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
  • anonymous
Yeahh it would. The trial and error method isn't 100% accurate but it's quite close
Jim766
  • Jim766
for the 2nd one, 9/3 what exponent can make each number its reciprocal
Jim766
  • Jim766
^ 9/3 = 3
ChillOut
  • ChillOut
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
  • ChillOut
Thanks for the help too, @Shawna.marie
anonymous
  • anonymous
Nytime:)
IrishBoy123
  • IrishBoy123
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
  • anonymous
Omg that is like ninja status:)

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