Where do I go wrong in solving this mathematical expression?


I was not sure if I should have chosen “Off-topic” or this “Mathematical” section, so please move post to appropriate section.

For now it is not a programming question I have, but more about how to solve this equation for ρ:


I’ve done the steps I am sure of, to get:


Then I know I would have to use some logarithm to get rid of the exponent:


Then I found a log rule stating that ln(x/y) = ln(x) - ln(y):


And to cancel the log I re-raise to an exponent and get the following expression:


It seems though that I have made a mistake somwhere since wolfram alpha returns:

Where ρ_0 is multiplied on, instead of added too.

If someone would be kind enough to explain to me where my mistake lies, I would really appreciate it :slight_smile:

Kind regards

e^{a+b} = e^a e^b :wink:

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Ah okay, got it!

I should have raised the whole RHS to exp, and not the terms individually. So this is wrong, it should have been the equation below:


And then the equation you wrote holds and I get the right answer :slight_smile:

Thank you!