1.
3*2^x-2^(x-1)+5*2^(x-2)=120
3*2^x-(2^x)/2+5*(2^x)/4=120 |*4
12*2^x-2*2^x+5*2^x=480
15*2^x=480 | :15
2^x=32
x=log2(32)
x=5
2.
4^x+2^(x+1)-80=0
2^(2x)+2*2^x=80
2^x=t (t>0)
t^2+2t-80=0
D=4+320=324
t1=(-2+18)/2=8
t2=(-2-18)/2= -10(t>0)
2^x=8
x=log2(8)
x=3
3.
log4(x-3)-1=log4(x-6)
ОДЗ:
x-3>0, x>3
x-6>0, x>6
log4(x-3)=1+log4(x-6)
log4(x-3)=log4(4)+log4(x-6)
x-3=4x-24
3x=21
x=7