Question

решить ср по логарифмам,35 балов!Срочно

Answer 1

A1. log(2)81 / log(2)3 = log(3)81 = 4

A2. a) log(5)(2x+1) + log(5)(16x-7) = 3

log(5)((2x+1)*(16x-7)) = 3

log(5)((32x^2+2x-7)) = 3

32x^2+2x-7 = 5^3 = 125

32x^2+2x-132 = 0

D<0 ⇒ Уравнение не имеет решения.

b) log(3)(5x+1) - log(3)(x+1) = 1

log(3)((5x+1)/(x+1)) = 1

(5x+1)/(x+1) = 3

5x+1 = 3x+3

2x = 2

x = 1

B1. lg(x+2) =  lg(5x+1) -  lg(4+2x)

lg(x+2) =  lg((5x+1)/(4+2x))

x+2 = (5x+1)/(4+2x)

5x+1 = (x+2)(4+2x)

2x^2+5x-7=0

D=81

x1 = 1

x2 = -3,5