x=1
Объяснение:
y= log₉(x²/4)
y=1-log₃(5+x)
x²/4>0⇒x≠0
5+x>0, x>-5
x∈(-5; 0)∪(0: +∞)
log₉(x²/4)=1-log₃(5+x)
log₃x-log₃2=1-log₃(5+x)
log₃x+log₃(5+x)=log₃3+log₃2
log₃(x·(5+x))=log₃(2·3)
log₃(x²+5x)=log₃6
x²+5x=6
x²+5x-6=0
x²-x+6x-6=0
x(x-1)+6(x-1)=0
(x-1)(x+6)=0
x>-5⇒x+6>-5+6=1>0
x-1=0
x=1
Объяснение:
y= log₉(x²/4)
y=1-log₃(5+x)
x²/4>0⇒x≠0
5+x>0, x>-5
x∈(-5; 0)∪(0: +∞)
log₉(x²/4)=1-log₃(5+x)
log₃x-log₃2=1-log₃(5+x)
log₃x+log₃(5+x)=log₃3+log₃2
log₃(x·(5+x))=log₃(2·3)
log₃(x²+5x)=log₃6
x²+5x=6
x²+5x-6=0
x²-x+6x-6=0
x(x-1)+6(x-1)=0
(x-1)(x+6)=0
x>-5⇒x+6>-5+6=1>0
x-1=0
x=1