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

Question

asked Sep 4, 2018 171k views

1 Answer

Carl Suster · Answer 1 · 2018-09-10T17:05:45+0000

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

First note that for both sides to be defined, we require
x^2+x+5>0

and

. The first condition is met for all

, and the other requires that
$x<\frac13$ .

Now,

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

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

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