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toadytica305

  • 2 years ago

I need help with this log function... 2^2x +^x-12=0

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  1. toadytica305
    • 2 years ago
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    [2^2x +2^x-12=0\]

  2. hartnn
    • 2 years ago
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    put 2^x = y i think you mean \[2^{2x} +2^x-12=0\]

  3. hartnn
    • 2 years ago
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    \[(2^{x})^2 +2^x-12=0 \\ 2^x=y \implies y^2+y-12=0\] can you solve this quadratic in y ?

  4. toadytica305
    • 2 years ago
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    Didn't think of doing it that way.. I'll try it now

  5. hartnn
    • 2 years ago
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    ask if you get stuck anywhere..

  6. toadytica305
    • 2 years ago
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    I get -7/2 and 3...

  7. hartnn
    • 2 years ago
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    y^2+y-12=0 (y+4)(y-3)=0 y=-4,3 what you got -7/2 and 3 for ? x ?

  8. toadytica305
    • 2 years ago
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    Yup

  9. hartnn
    • 2 years ago
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    did you get how y=-4,3 ?

  10. toadytica305
    • 2 years ago
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    The answer is supposed to be ln3/ln2

  11. toadytica305
    • 2 years ago
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    Yes, that part i did.. and i plugged those Y's into X

  12. hartnn
    • 2 years ago
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    \(2^x=3 \\ \ln 2^x=\ln 3 \\ x \ln 2 = \ln 3 \\ x= \ln3/ \ln 2\)

  13. toadytica305
    • 2 years ago
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    Just saw where I messed up.. I pugged the Y's into 2^x... Thanks!!

  14. hartnn
    • 2 years ago
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    welcome ^_^

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