( log₈ 9 + log₀․₂₅ 3 ) × ( log₍1/3₎ 0.5 + log₉ 16 ) + ( log₄ 125 / log₈ 5 )

log₈ 9 + log₀․₂₅ 3
log₈ 9 = (2/3)·log₂ 3
log₀․₂₅ 3 = −(1/2)·log₂ 3

(2/3 − 1/2) log₂ 3 = (1/6)·log₂ 3

log₍1/3₎ 0.5 + log₉ 16
log₍1/3₎ 0.5 = log₃ 2
log₉ 16 = 2·log₃ 2

log₃ 2 + 2log₃ 2 = 3log₃ 2

(1/6)·log₂ 3 × 3·log₃ 2
= (1/2)(log₂ 3 · log₃ 2)
= 1/2

(log₄ 125) / (log₈ 5)
log₄ 125 = (3/2) log₂ 5
log₈ 5 = (1/3) log₂ 5

(3/2) ÷ (1/3) = 9/2

1/2 + 9/2 = 10/2 = 5