2log3(x-1)= log3(4x+1)

Question

2log3(x-1)= log3(4x+1)

Answer 1

2log3(x-1)= log3(4x+1)                     {x-1>0              {x>0

log3(x-1)^2=log3(4x+1)                    {4x+1>0            {x>-1/4

(x-1)^2=4x+1

x^2-2x+1=4x+1                                 x>0

x^2-6x=0                                         

x(x-6)=0

x=0 -не подходит, т.к. х>0     или      x=6>0

 

Ответ: 6

Answer 2

log₃(x-1)²=log₃(4x+1)

(x-1)²=4x+1

x²-2x+1-4x-1=0

x²-6x=0

x(x-6)=0

x₁=0

x₂=6