I'm doing some math test prep for Math 126, but I'm confused as to how \(\frac{-3}{1-e^4}\) is the answer?

The Problem:

ln (x+3) - ln x = 4

I tried to condense the left side so that I'd have \(ln(\frac{x+3}{x})=4\) and then raise both sides to the power of \(e\), but that doesn't seem to work.

I thought that I could use this condensing and power raising technique since I was able to get the correct answer for the problem right after with this method, which by the way was: \({log}_{2}x+{log}_{2}(x+6)=4\)

Is there something different I must do with natural log equations or was I on the right track?

Help would be greatly appreciated, thanks!

Guest Apr 25, 2018