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Math Help - Logarithm: Fractional exponents

  1. #1
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    Question Logarithm: Fractional exponents

    1. x2/3=4 //Really dont know T_T

    2. 5x=square root of 5
    ~ 5x= 5 * 51/2
    ~ 5x = 53/2 //How did 3/2 happen? - .-


    I dont know how to solve the ff fractional fractional exponents. please explain to me step by step. T_T
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  2. #2
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    Re: Logarithm: Fractional exponents

    Quote Originally Posted by KerkLu View Post
    1. x2/3=4 //Really dont know T_T

    2. 5x=square root of 5
    ~ 5x= 5 * 51/2
    ~ 5x = 53/2 //How did 3/2 happen? - .-


    I dont know how to solve the ff fractional fractional exponents. please explain to me step by step. T_T
    First of all, in question 2, you can not turn \displaystyle \sqrt{5} into \displaystyle 5\sqrt{5}. Are you sure you wrote down the question properly?
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    Re: Logarithm: Fractional exponents

    ohh sorry, my mistake xD That was still 5 square root of 5. Thanks
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    Re: Logarithm: Fractional exponents

    It's because \displaystyle \sqrt{5} = 5^{\frac{1}{2}}, so \displaystyle 5\sqrt{5} = 5^1 \cdot 5^{\frac{1}{2}} = 5^{1 + \frac{1}{2}} = 5^{\frac{3}{2}}.
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    Re: Logarithm: Fractional exponents

    I forgot about that , tnx but how about no.1?
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  6. #6
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    Re: Logarithm: Fractional exponents

    x^2/3 = 4
    Both the sides should be raised to the power os 3/2
    Thus we have [x^2/3]^3/2 = 4^3/2 that gives x = [4^1/2]^3=2^3= 8
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