Question 1140061: If 2^x = 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 KMST(5328)   (Show Source):
You can put this solution on YOUR website! ONE WAY:
We know  ,  and  because otherwise they would make the denominators zero, and the expression  would not exist as a real number.
As  and  ,
if  ,
 ,
and  ,  , and  .
Also  , which means  , and  .
You could also talk about taking logarithms base 2.\ to get to the same conclusions.
Then, substituting into  , we get
Multiplying both sides of the equation times the non-zero number  ,
we get the equivalent equation
Then, as ,  ,
and as , 
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