Question

Solve ln (x+1)=ln x+1 for x

Answer 1

This might make it look easier:

\(ln(x+1) = ln(x) + ln(e) \)

Answer 2

move logs to one side
combine logs

\[\ln (x+1) -\ln x = 1\]
\[\ln \frac{x+1}{x} = 1\]
take "e" raised to both sides
or change to exponential form
\[\frac{x+1}{x} = e\]
\[x+1 = ex\]
\[1 = ex -x\]
\[x = \frac{1}{e-1}\]

Answer 3

@tkhunny , that would save a couple of steps, i didn't think of that

Answer 4

Thank you both

Answer 5

I am always delighted when unique answers don't care how you find them. ALWAYS keep your mind open for alternatives.