Verified answer

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Verified answer

15

log(2) (x-1)=2

x>1

x-1 = 2^2

x=5

16

log(3) √(x-5) + log(3) √(2x-3) = 1

одз x-5>0 x>5  

2x-3>0 x>3/2

x∈(5 +∞)

log(3) √(x-5)√(2x-3) = 1

(x-5)(2x-3)=3

2x² - 3x - 10x + 15 = 9

2x² - 13x + 6 = 0

D = 169 - 48 = 121

x12=(13+-11)/4 = 6    1/2

1/2 < 5 не подходит

x=6

14

1/(5 + lg x) +  2/(1 - lg x) = 1

одз x>0

x<>10^-5  x<> 10

lg x = t

1/(5+t) + 2/(1-t) = 1

1 - t + 2(5 + t) = (5+t)(1-t)

1 - t + 10 + 2t = 5 - 5t + t - t²

t² + 5t +6 = 0   D=25-24 = 1

t12=(-5+-1)/2 = -2  -3

t=-2 lg x = -2  x=1/100  

t=-3 lg x = -3   x=10^-3=1/1000

x=1/100  1/1000