Решить систему: log_y (x) - log_2 (y^2) = 1, log_4 (x) - log_4 (y) = 1.

Log (4) x-log (4) y=1⇒log (4) x/y=1⇒x/y=4⇒x=4y

log (y) 4y-log (2) y²=1

1+2log (y) 2 - 2/log (y) 2=1

log (y) 2+2log² (y) 2-log (y) 2-2=0 log (y) 2≠0

2log² (y) 2=2

log² (y) 2=1

log (y) 2=-1 U log (y) 2=1

y1=1/2 U y2=2

x1=2 U x2=8

(2; 1/2) U (8; 2)