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Hey! I'm new to sage and I'm trying to see how complex are the calculations that I can express in SageMath. So I considered the following example, the comparison between the likelihood of two normals with different means but same variance:

$$\dfrac{1}{\sigma\sqrt{2\pi} } \exp{\left(-\dfrac{(x-\mu_1)^2}{2\sigma^2}\right)} = \dfrac{1}{\sigma\sqrt{2\pi} } \exp{\left(-\dfrac{(x-\mu_2)^2}{2\sigma^2}\right)}$$

I know that the answer must be $\mu_1 = \mu_2$. Can I solve it with SageMath? I tried:

x, mu1, mu2, sigma = var('x, mu1, mu2, sigma')
exp((0.5/sigma)*(x-mu1)^2)==exp((0.5/sigma)*(x-mu2)^2)

and

solve(exp((0.5/sigma)*(x-mu1)^2)==exp((0.5/sigma)*(x-mu2)^2))

but that doesn't seem to work. Is it possible to do so in sagemath? Thanks!!