# Where is this number coming from?

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.

• $e^{x\ln (2)}=e^{x\ln (3)+2in\pi}$ and now consider what $e^{i\theta}$ represents. Nov 2 '18 at 16:41
• wouldn't be easier to divide both sides by $3^x$ and conclude that $x=0$ is the only solution in real numbers? WolframAlpha gives you complex solutions Nov 2 '18 at 16:41
• The user did tag this question as complex-numbers. Nov 2 '18 at 16:47
• Which may very well come from the fact that Wolfram Alpha gave complex numbers as results to the OP. Nov 3 '18 at 2:25