2^x = 4^y = 8^z ;;;; x=2y=3z;;;

[1/2x] + [1/4y] + [1/4z] = 4

multiply 4 both sides ;;

[2/x] + [1/y] + [1/z] = 16 ;;;

[2/x] + [2/x] + [3/x] = 16 ;;;

[7/x] = 16 ;;;

x= 7/16 ;;;

+1 vote

If 2^(x) = 4^(y) = 8^(z) and 1/(2x) + 1/(4y) + 1/(4z) = 4 then what is the value of x?

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2^x=4^y=8^z......................................................given

2^x=2^(2y)=2^(3z)

x=2y=3z

x.............................................................................(i)

y=x/2.....................................................................(ii)

z=x/3....................................................................(iii)

[1/2x+1/4y+1/4z]..............................................given

{(1/2x)+[1/4(x/2)]+[1/4(x/3)]........................from (i),(ii),(iii)

Simplify

x=7/16

Ans is 7/16

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