Where is this number coming from?

Question

I am trying to solve $2^x = 3^x$ for $x$.

Now I plug this into WolframAlpha and the steps to the solution are the following:

• Take natural log of both sides which leaves me with this (according to them):

$$ x\ln(2)= x\ln(3) + 2in\pi $$

What I don't understand is where is this $2in\pi$ coming from?

Thank you very much for your time and help.

Answer 1

It results from:

• rewriting your equation as $e^{xln2} = e^{xln3}*1$
• the property $1 = e^{i2n\pi}$ of complex exponentials (see https://en.wikipedia.org/wiki/Euler%27s_formula)