2 x power = 3 y power = 5 Z power compare 2x 3Y 5Z size

2 x power = 3 y power = 5 Z power compare 2x 3Y 5Z size

∵ 2 ^ x = 3 ^ y both sides are logarithms with respect to e, so there is xln2 = yln3 ∵ X / y = Ln3 / LN2 ∵ 2x / 3Y = 2ln3 / 3ln2 ≈ 1.057 ∵ 1 ∵ 2x > 3Y ∵ 3; 3Y = 5 ^ Z both sides are logarithms with respect to e, so there is yln3 = zln5 ∵ Y / z = LN5 / Ln3 ∵ 3; 3; 3Y / 5Z = 3ln5 / 5ln3 ≈ 0.880 ∵ 1 ∵ 3; 3; 3; 3; 3Y ? 5; 5; 2; 2; 2; 2; 2