Log16 sin p/12 + log16 cos p/12 чему равно

Question

Log16 sin p/12 + log16 cos p/12 чему равно

Answer 1

Log₁₆sin(π/12)+log₁₆cos(π/12)=log₁₆[sin(π/12)cos(π/12)]=(1/2)log₄[(1/2)sin(π/6)]=
(1/2)log₄[(1/2)×(1/2)]=(1/2)log₄(1/4)=-(1/2)log₄4=-1/2