Log7 (5+4x-x^) + logx-1 3

1) ОДЗ x>0 U x≠1⇒x∈ (0; 1) U (1; ∞) log (7) x - 1=6/log (7) x

(log (7) x) ² - log (7) x-6=0

log (7) x=a

a²-a-6=0

a1+a2=1 U a1*a2=-6

a1=-2⇒log (7) x=-2⇒x=1/49

a2=3⇒log (7) x=3⇒x=343

2) ОДЗ x>0 U x≠1 U x≠1/2 U x≠1/4⇒x∈ (0; 1/4) U (1/4; 1/2) U (1/2; 1) U (1; ∞)

1/log (2) x * 1 / (log (2) x + 1) = 1 / (log (2) + 2)

log (2) x * (log (2) x + 1) = log (2) x+2

(log (2) x) ²+log (2) x-log (2) x=2

(log (2) x) ²=2

log (2) x=-√2⇒x=1/2 ^{ / sqrt{2} }

log (2) x=√2⇒x=2 ^{ / sqrt{2} }

3) ОДЗ x>0

0,4 ^{lg^2x-1} = 0,4 ^{2lgx^2+4}

lg²x-1=4+4lgx

lg²x-4lgx-5=0

lgx=a

a²-4a-5=0

a1+a2=4 U a1*a2=-5

a1=-1⇒lgx=-1⇒x=0,1

a2=5⇒lgx=5⇒x=100000