Question

log2x+5logx2=6
Найти x

Answer 1

Log2x+5logx2=6

Log2x+5/log2x=6

Х>0; х≠1

Log2x=t

t+5/t-6=0 / *t

t^2-6t+5=0

Д=36-20=16

t1=(6+4)/2=5

t2=(6-4)/2=1

Log2x=5

Log2x=log2 2^5

X=2^5=32

Log2x=1

Log2x=log2 2

X=2

Ответ: 2; 32