SOLUTION: If 2ˣ = 4^y = 8^z and 1/2x + 1/4y + 1/8z = 22/7, show that: x = 7/16, y = 7/32 and z = 7/48

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Question 1206509: If 2ˣ = 4^y = 8^z and 1/2x + 1/4y + 1/8z = 22/7, show that:
x = 7/16, y = 7/32 and z = 7/48
Answer by ikleyn(52855)   (Show Source): You can put this solution on YOUR website!
.
If 2ˣ = 4^y = 8^z and 1/2x + 1/4y + 1/8z = 22/7, show that
x = 7/16, y = 7/32 and z = 7/48
~~~~~~~~~~~~~~~~~~~~~~ 

From the given part   =  = ,  we have

     =  = .


It gives us  x = 2y = 3z,  or  y = ,  z = .


Now substitute it into equation

     +  +  = .


You will get

     +  +  = ,

or

     +  +  = ,

     +  +  = ,

     = ,

     = ,

    x =  = .


Then   y =  = ,  z =  = ,   QED.

Solved.



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