1.
a) og₃81-lne+lg1000=log₃3⁴-1+lg10³=4-1+3=6.
b) 2*log₇16/((log₃(√10+1)+log₃(√10-1))*log₇2)=2*log₇2⁴/log₃*((√10)²-1²)*log₇2) =8*log₇2/(log₃9*log₇2)=8/(log₃3²)=8/2=4.
2.
a) 4ˣ-3*2ˣ+2=0
2²ˣ-3*2ˣ+2=0
2ˣ=t
t²-3t+2=0 D=1
t₁=1 2ˣ=1 x₁=0
t₂=2n 2ˣ=2 x₂=1
b) log₂x+6*log₄x=8 ОДЗ: x>0
log₂x+6*log₂²x=8
log₂x+(6/3)*log₂x=8
log₂x+3*log₂x=8
4*log₂x=8
log₂x=2
x=2²
x=4.