1
a)4-1+3=6
b)2log(7)16/[log(3)(10-1)*log(7)2]=2*4log(2)7/[log(3)9*log(7)2]=8/log(3)9=8/2=4
2
a)2^x=t
t²-3t+2=0
t1+t2=3 U t1*t2=2
t1=1⇒26x=1⇒x=0
t2=2⇒26x=2⇒x=1
b)log(20x+6(log(2)x)/2=8
log(20x+3log(2)x=8
4log(2)x=8
log(2)x=2
x=4
3
a)3^x*(3²-2*3+1)<12<br>4*3^x<12<br>3^x<3<br>x<1<br>x∈(-∞;1)
b)x>0
log(0,5)x=t
t²+3t-4≤0
t1+t2=-3 U t1*t2=-4
t1=-4 U t2=1
-4≤t≤1
{log(0,5)x≥-4⇒x≤16
{log(0,5)x≤1⇒x≥1/2
x∈[1/2;16]
6
5*6/5*(5/6)^x-9*(5/6)^-x +3=0
(5/6)6x=t
6t-9/t +3=0
6t²+3t-9=0
2t²+t-3=0
D=1+24=25
t1=(-1-5)/4=-3/2⇒(5/6)^x=-3/2 нет решения
t2=(-1+5)/4=1⇒(5/6)^x=1⇒x=0