Question

log5(6x-1)=log5(x+3). log2(x la puterea a doua - 2x)=log2(x-2). log3(2x+1)=log3(9x+5)​

Answer 1

Răspuns:

Explicație pas cu pas:

1) Conditii: 6x -1 >0 si x+3 > 0

x > 1/6 si x > -3

Deci x in(1/6, +inf)

Log5(6x-1)=log5(x+3)

6x -1 = x +3

5x = 4,  x = 4/5 convine

2) Conditii:

x^2 - 2x > 0 si x - 2 > 0

x(x-2)>0 x in (-inf, 0)U(2, +inf) si x > 2

Deci x in (2, +inf)

log2(x^2 -2x) = log2(x-2)

x^2 - 2x = x - 2  

x^2 -3x +2 = 0

delta = 9 -8 = 1

x1,2 = (3 +- 1)/2

x1 = 2/2 = 1 nu convine

x2 = 4/2 = 2 nu convine

Fara solutie

etc.