Question

Log2^2x^2 + 6 log 0,25 x-1=0

Answer 1

log22 x2 + 6log0,25 x - 1 = 0

(2log2 x)2 + 6log2^(-2) x - 1 = 0

4(log2 x)2 - (6/2)* log2 x - 1 = 0

4(log2 x)2 - 3log2 x - 1 = 0

Замена: log2 x = t

4t2 - 3t - 1 = 0

t= 1; t= -1/4

log2x = 1 x1=2

log2x = -1/4 x2= 2-1/4 = 1 / 4√2