MHB Solve 2000 = 4𝐾^0.75 * L^0.25 - 5000(10/3)^.75

[markosheehan]

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

 

[MarkFL]

Re: equation

We are given to solve for $L$:

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

Divide through by 4:

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

We are told:

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

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

Hence:

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