Question

log1/4(5x-x^2)+5log3 (1) <0

Answer 1

log₁/₄(5x-x²)+5log₃1<0
ОДЗ: 5x-x²>0, x∈(0;5)
log₁/₄(5x-x²)+5*0<0
log₁/₄(5x-x²)<0, 0=log₁/₄(1/4)⁰=log₁/₄1
log₁/₄(5x-x²)<log₁/₄1
0<(1/4)<1, меняем знак неравенства
5x-x²>0
x∈(0:5)