1) log5(4x+17)=log5(x4-3)+1 2) log3(2x+1)=log3(13)+1 3) log3(x^2-3)+log3(2)=log3(6x-10). Created by dofii75. algebra-ru

1) log5(4x+17)=log5(x4-3)+1 2) log3(2x+1)=log3(13)+1 3) log3(x^2-3)+log3(2)=log3...

July 2022 1 4 Report

1) log5(4x+17)=log5(x4-3)+1
2) log3(2x+1)=log3(13)+1
3) log3(x^2-3)+log3(2)=log3(6x-10)

Answers & Comments

MizoriesKun 1) log5(4x+17)=log5(4x-3)+1 ОДЗ 4х-7>0 x>7/4 ,4x-3>0 x>3/4
  log₅(4x+17)=log₅(4x-3)+log₅ 5
log5(4x+17)=log5(4x-3)*5
log5(4x+17)=log5(20x-15)
4х+17=20х-15
16х=32
х=2

  log₃(2x+1)=log₃(13)+log₃3 ОДЗ 2х+1>0 x> -1/2
   log₃(2x+1)=log₃(13*3)
log₃(2x+1)=log₃39
2x+1=39
2x=38
x=14

3) log₃(x²-3)+log₃(2)=log₃(6x-10) ОДЗ х²-3>0 x>√3 ,x<-√3
6x-10>0 x>5/3
  log₃(x²-3)*2=log₃(6x-10)
2x²-6=6x-10
2x²-6x+4=0 /2
   x²-3x+2=0
D=9-8=1
x₁=(3+1)/2=2
x₂=(3-1)/2=1 не подходит под ОДЗ

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