Question

PlzhelpHow do i do this step by step logarithmic equation
ln(x2+x+5)=ln( - 3x+1)

Answer 1

`\ln(x^2+x+5)=\ln(-3x+1)`

First note that for both sides to be defined, we require
`x^2+x+5>0` and
`-3x+1>0`. The first condition is met for all
`x`, and the other requires that
`x<\frac13`.

Now,


`e^(\ln(x^2+x+5))=e^(\ln(-3x+1))`

`x^2+x+5=-3x+1`

`x^2+4x+4=0`

`(x+2)^2=0`

`x=-2`

Since
`-2<\frac13`, this is the only solution.