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