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  1. MHB Apprentice

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    #1
    can someone solve 2000 = 4𝐾^0.75 * L^0.25 where k=3/10 L. i tryed to solve this by adding the powers 2000=4(3/10 L^1) however i get an answer of 5000/3 which is not the correct answer the correct answer is 5000(10/3)^.75

  2. Pessimist Singularitarian
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    #2
    We are given to solve for $L$:

    $ \displaystyle 2000=4K^{\frac{3}{4}}L^{\frac{1}{4}}$

    Divide through by 4:

    $ \displaystyle 500=K^{\frac{3}{4}}L^{\frac{1}{4}}$

    We are told:

    $ \displaystyle K=\frac{3}{10}L$:

    $ \displaystyle 500=\left(\frac{3}{10}L\right)^{\frac{3}{4}}L^{\frac{1}{4}}=\left(\frac{3}{10}\right)^{\frac{3}{4}}L$

    Hence:

    $ \displaystyle L=500\left(\frac{10}{3}\right)^{\frac{3}{4}}$

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