Объяснение:
1.
log5(x)+logx(25)=3 одз:х∈(0;1)⋃(1;+∞)
log5(x)+log5(25)/log5(x)=3
log5(x)+log5(5²)/log5(x)=3
log5(x)+2/log5(x)=3
t=log5(x)
t+2/t=3
t²-3t+2=0
t=1
t=2
log5(x)=1
log5(x)=2
x=5¹=5
x=5²=25
x∈(0;1)⋃(1;+∞)
ответ: х=5; х=25
2.
log2(x)•log4(x)•log8(x)=36 ; x>0
log2(x)•log2(x)/log2(4)•log2(x)/log2(8)=36
log³2(x)/(2•3)=36
log³2(x)=216
log³2(x)=6³
log2(x)=6
x=2⁶=64
ответ: х=64
3.
ответ: 1 ; 2
Copyright © 2025 SCHOLAR.TIPS - All rights reserved.
Answers & Comments
Объяснение:
1.
log5(x)+logx(25)=3 одз:х∈(0;1)⋃(1;+∞)
log5(x)+log5(25)/log5(x)=3
log5(x)+log5(5²)/log5(x)=3
log5(x)+2/log5(x)=3
t=log5(x)
t+2/t=3
t²-3t+2=0
t=1
t=2
log5(x)=1
log5(x)=2
x=5¹=5
x=5²=25
x∈(0;1)⋃(1;+∞)
ответ: х=5; х=25
2.
log2(x)•log4(x)•log8(x)=36 ; x>0
log2(x)•log2(x)/log2(4)•log2(x)/log2(8)=36
log³2(x)/(2•3)=36
log³2(x)=216
log³2(x)=6³
log2(x)=6
x=2⁶=64
ответ: х=64
3.
ответ: 1 ; 2