January 4th, 2017, 08:12 AM  #1 
Member Joined: May 2016 From: Ireland Posts: 96 Thanks: 1  equation
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

January 4th, 2017, 08:26 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,900 Thanks: 1094 Math Focus: Elementary mathematics and beyond 
What variable are you solving for? Are you sure the equation is typed correctly?

January 4th, 2017, 09:12 AM  #3  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,804 Thanks: 971  Quote:
Also, it is basic that adding powers works ONLY this way: a^x * a^y = a^(x+y) a^x * b^y does NOT equal (ab)^(x+y) So for your problem, you CANNOT add powers. Is your math teacher drunk half the time?  
January 4th, 2017, 11:38 AM  #4  
Senior Member Joined: May 2016 From: USA Posts: 1,256 Thanks: 523  Quote:
See greg's question. This looks like a a CobbDouglas function. $2000 = 4 * K^{3/4} * L^{1/4}\ and\ K =0.3L \implies$ $2000 = 4 * \left ( \dfrac{3}{10} * L \right )^{3/4} * L^{1/4} = 4 * \left ( \dfrac{3}{10} \right)^{3/4} * L^{3/4} * L^{1/4} = 4L * \left ( \dfrac{3}{10} \right)^{3/4} \implies$ $L = \dfrac{2000}{4} \div \left ( \dfrac{3}{10} \right)^{3/4} = 500 \div \dfrac{3^{3/4}}{10^{3/4}} = 500 * \dfrac{10^{3/4}}{3^{3/4}} \implies$ $L = 500 * \left ( \dfrac{10}{3} \right )^{3/4}.$ We have no clue where the 5000 came from.  
January 5th, 2017, 06:29 AM  #5 
Member Joined: May 2016 From: Ireland Posts: 96 Thanks: 1 
thanks for answers and my teacher isnt good


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