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Math Help - contract this log

  1. #1
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    contract this log

    Hey guys how do you contract this log? -4log√y + 3/2log9x⁴+ Żlog3√z
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  2. #2
    MHF Contributor Unknown008's Avatar
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    -4 log\sqrt{y} + \frac32 log(9x^4) + \frac12 log(3\sqrt{z})

    Hm... use this rule:

    a\ log (x) = log(x^a)

    log\sqrt{y^{-4}} + log(9x^4)^\frac32 + log(3\sqrt{z})^\frac12

    Rewrite all the powers

    log((y^{\frac12})^-4) + log(9x^4)^{\frac32} + log(3z^\frac12)^{\frac12}

    Simplify;

    log(y^{-2}) + log(3x^2)^3 + log(3^{\frac12}z^\frac14)

    log(\frac{1}{y^2}) + log(27x^6) + log(3^{\frac12}z^\frac14)

    Now, combine the terms since they have a common base.

    log((\frac{1}{y^2})(27x^6)(3^{\frac12}z^\frac14))

    Simplify...

    log (\frac{27 \sqrt{3}x^6  z^{\frac14} }{y^2})
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