SOLUTION: 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.

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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