1.
a) log₂32+lne-lg100=log₂2⁵+1=lg10²=5*log₂2+1-2*lg10=5+1-2=4.
b) (log₂(√5-1)log₂+log₂(√5+1))*log₃49/log₃7=
=log₂((√5-1)(√5+1))*log₃7²log₃7=log₂((√5)²-1²)*log(2*log₃7/log₃7)=
=2*log₂(5-1)=2*log₂4=2*log₂2²=2*2*log₂2=2*2=4.
2.
a) (1/9)ˣ+8*(1/3)ˣ-9=0
(1/3)²ˣ+8*(1/3)ˣ-9=0
(1/3)ˣ=t >0
t²+8t-9=0 D=100
t₁=1 (1/3)ˣ=1 (1/3)ˣ=(1/3)⁰ x=0
t₂=-9 ∉
Ответ: x=0.
b) log₃x+4*log₉x=9
log₃x+4*log₃²x=9
log₃x+√4*log₃x=9
log₃x+2*log₃x=9
3*log₃x=9
log₃x=3
x=3³
x=27.
Ответ: x=27.