x y z都不=0且為實數 8的x次方=9的y次方=6的z次 x分之2+y分之3=z分之k 求k?

8ˣ = 9ʸ = 6ᶻ
6ᶻ = 2³ˣ , 6ᶻ = 3²ʸ
6 ᶻ/⁽³ˣ⁾= 2 , 6 ᶻ/⁽²ʸ⁾= 3
6 ᶻ/⁽³ˣ⁾ × 6 ᶻ/⁽²ʸ⁾ = 2 × 3
6 ᶻ/⁽³ˣ⁾⁺ ᶻ/⁽²ʸ⁾= 6¹
z/(3x) + z/(2y) = 1
2/x + 3/y = 6/z
k/z = 6/z
k = 6

8^x=9^y=6^z
x log 8=y log 9=z log 6
x:y:z=(log 9)(log 6):(log 8)(log 6):(log 8)(log 9)
2/x +3/y=k/z
2/[(log 9)(log 6)+3/[(log 8)(log 6)]=k/[(log 8)(log 9)]
k=6