Log^2 x+2log x = (1/2) ^log

8 8 0.5^3

sin^4 / alpha - cos^4 / alpha + cos^2 / alpha

log₈²x+2*log₈x = (1/2) ^log₀,₅3 ОДЗ: x>0

log ₈²x+2*log₈x = (0,5) ^log₀,₅3

log₈²x+2*log₈x=3

log₈²x+2*log₈x-3=0

Пусть log₈x=t ⇒

t²+2t-3=0 D=16

t₁=1 ⇒ log₈x=1 x₁=8¹=8.

t₂=-3 ⇒ log₈x=-3 x₂=8⁻³=1/512.

Ответ: x₁=8 x₂=1/512.

sin⁴α-cos⁴α+cos²α = (sin²α-cos²α) (sin²α+cos²α) + cos²α=

= (sin²α-cos²α) * 1+cos²α=sin²α-cos²α+cos²α=sin²α.