8*(3/2)^2x-30*(3/2)^x+27=0
(3/2)^x=t
8t²-30t+27=0
D1=15²-8*27=225-216=9
t1=(15+3)/8=18/8=9/4 t2=(15-3)/8=12/8=3/2
(3/2)^x=9/4 (3/2)^x=3/2
(3/2)^x=(3/2)² x=1
x=2
log(2)x+6*1/2log(2)x+9*1/3log(2)x=14
log(2)x+3log(2)x+3log(2)x=14
7log(2)x=14
log(2)x=2
x=2²=4
4) log(9)(6√6-15)²+log(27)(6√6+15)³=2
log(3)(6√6-15)+log(3)(6√6+15)=log(3)(6√6-15)(6√6+15)=log(3)((6√6)²-15²=log(3)(216-225)=log(3)9=2