1.
a)
(2√3-5)²+4√3(6-√3)=12-20√3+25+24√3-12=4√3
b)
4/(√6-2)=4(√6+2)/(√6-2)(√6+2)=4(√6+2)/(6-4)=4(√6+2)/2=2(√6+2)
2.
a)
log5 √5-log5 125=log5 5^1/2-log5 5³=1/2log5 5-3log5 5=1/2·1-3·1=1/2-3=-2 1/2
b)
a=log3 (1/9)=log3 3^-2=-2log3 3=-2·1=-2
b=log3 3=1
c=log3 (1/27)=log3 3^-3=-3log3 3=-3·1=-3
c < a < b
c)
log1/3 27 /log3 √27=log3^-1 (3³)/log3 (27^1/2)=-log3 3³/log3 (3³)^1/2=-3log3 3/log3 3^3/2=-3/(3/2)=-3·2/3=-2
