8=2³ = ((√2)²)³ = (√2)⁶
16=2⁴ = ((√2)²)⁴ = (√2)⁸
log₈ a³ = log(√₂)⁶ a³ = 3*(¹/₆) log√₂ a = ¹/₂ log√₂ a = log√₂ a^(¹/₂)
log₁₆ a = log(√2)⁸ a = ¹/₈ log√₂ a
log√₂ a^(¹/₄) - log√₂ a^(¹/₂) = log√₂ (a^(¹/₄) : a^(¹/₂)) = log√₂ a^(⁻¹/₄) =
¹/₈ log√₂ a ¹/₈ log√₂ a ¹/₈ log√₂ a
= ⁻¹/₄ log√₂ a = -¹/₄ * 8 = -2
¹/₈ log√₂ a
Ответ: -2