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Math Help - How do I solve this?

  1. #1
    Member
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    How do I solve this?

    The question wants me to solve:
    3^(x+2) - 4 = 12

    So:
    3^(x+2) = 8

    What do I do next?

    Any help is appreciated.
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  2. #2
    Senior Member Dinkydoe's Avatar
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    I hope you are familiar with logarithms

    Anyway: Observe that log(8)/log(3) = x+2
    And this is equivalent to: log(8)/log(3)-2 = x
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  3. #3
    Junior Member
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    Quote Originally Posted by iluvmathbutitshard View Post
    The question wants me to solve:
    3^(x+2) - 4 = 12

    So:
    3^(x+2) = 8

    What do I do next?

    Any help is appreciated.
    3^{x+2} - 4 = 12

    Ok....hopefully this helps and you know the log properties

    3^{x+2}= 16

    \ln3^{x+2} = \ln 16

    (x+2)\ln3 = \ln 16

    This is one way, a little longer...

    x\ln3+2\ln3 = \ln 16

    x\ln3 = \ln 16 - 2\ln3

    x\ln3 = \ln (\frac{16}{9})

    x= \frac{\ln (\frac{16}{9})}{\ln3}

    Or going back to the line before my comment....

    (x+2)\ln3 = \ln 16

    x+2 = \frac{\ln 16}{\ln3}

    x = \frac{\ln 16}{\ln3}-2

    and both....

    x = \frac{\ln 16}{\ln3}-2 and x= \frac{\ln (\frac{16}{9})}{\ln3} = .5237190143....
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  4. #4
    Member
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    Thank you so much. This really helps.
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