Question

log^2 от 4 (64-x^2)-5log4(64-x^2)+6

Answer 1

ОДЗ: 64-х²>0. x∈(-8;8)
log₄²(64-x²)-5log₄(64-x²)+8=0
log₄(64-x²)=t
t²-5t+6=0
t₁=2, t₂=3
1. t₁=2, log₄(64-x²)=2, 64-x²=4², 64-x²=16, x²=48, x=4√3
4√3∈(-8;8)

2. t=3, log₄(64-x²)=3, 64-x²=4³, 64-x²=64. x=0
0∈(-8;8)
ответ: x₁=4 √3, x₂=0