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Math Help - two simple log questions

  1. #1
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    two simple log questions

    Hi everyone, just need help with two little questions:

    1. state as a single log in simplest form: \frac{1}{2}log_{a}x - \frac{2}{3}log_{a}y

    isn't this just log_{a}\frac{x^\frac{1}{2}}{y^\frac{2}{3}}



    2. solve for x in 5^{x^2-x} = 7

    is there an easier way than changing it to a quadratic, setting to 0 and solving?

    5^{x^2-x} = 7

    (x^2-x)log5 = log7

    x^2-x = \frac{log7}{log5}

    x^2-x-\frac{log7}{log5} = 0
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  2. #2
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    Quote Originally Posted by hello View Post
    Hi everyone, just need help with two little questions:

    1. state as a single log in simplest form: \frac{1}{2}log_{a}x - \frac{2}{3}log_{a}y

    isn't this just log_{a}\frac{x^\frac{1}{2}}{y^\frac{2}{3}}



    2. solve for x in 5^{x^2-x} = 7

    is there an easier way than changing it to a quadratic, setting to 0 and solving?

    5^{x^2-x} = 7

    (x^2-x)log5 = log7

    x^2-x = \frac{log7}{log5}

    x^2-x-\frac{log7}{log5} = 0
    1. Correct

    2. No quicker way that I know of. Should be easy enough to solve using the quadratic formula
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