How do you solve lnx=1ln(x+8)?

2 Answers
Aug 6, 2015

I found: x=4+16+e

Explanation:

Write it rearranging as:
ln(x)+ln(x+8)=1
use the fact that lnx+lny=ln(xy)
so:
ln[x(x+8)]=1
use the definition of log:
lnx=ax=ea
x(x+8)=e1
x2+8xe=0
using the Quadratic Formula:
x1,2=8±64+4e2=8±216+e2=
=4±16+e
so you get two solutions but one, 416+e, doesn't work when substituted into the original equation (it is a negative number, try it!) and you can discard it keeping only:
x=4+16+e

Aug 6, 2015

x=4±16+e

Explanation:

Rewriting the equation , it is ln x + ln(x+8) =1

ln x(x+8)=1

x2+8x=e

x2+8xe=0

x= 8±64+4e2

x=4±16+e