Where do I go wrong in solving this mathematical expression?

[Ahmed_Salih]

Hello!

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

Kind regards

[cvanaret]

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

[Ahmed_Salih]

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

Thank you!