Решите уравнение log 37 по основанию х, минус log x^2 по основанию 37 равно - 1

Log37 x=z

1/z-2z+1=0

-2z²+z+1=0

2z²-z-1=0

z1=1 log37 x=1 x=37

z2=-0.5 log37 x=-0.5 x=1/√37

Logx (37) - 2log37 (x) = - 1

1/log37 (x) - 2 log37 (x) = - 1

2log37 (x) ^2 - log37 (x) - 1 = 0

t = log37 (x)

2t^2 - t - 1 = 0

D = 1 + 8 = 9

t1 = (1+3) / 4 = 1

t2 = (1-3) / 4 = - 1/2

log37 (x) = 1 x = 37

log37 (x) = - 1/2 x = 1/корень (37)