You should probably consider the case of w=0 first, before you take logs or divide by it. In that case, every z works. I think it's nicer to simplify the answer to 1+(ln 2+2pi m i)/(ln w). It doesn't matter in this case, but you generally want to address the question of whether a mulivalued expression that appears multiple times has to use the same value each time., and just canceling them where appropriate avoids that question.
I get the allure of a power that doubles, but why drag it out with all the periodicity manipulations? Do the multiples of two pi enhance the allure or burden it with overdone pedantry? The principal branch ought to suffice.
It works if w & z are 2
You should probably consider the case of w=0 first, before you take logs or divide by it. In that case, every z works.
I think it's nicer to simplify the answer to 1+(ln 2+2pi m i)/(ln w). It doesn't matter in this case, but you generally want to address the question of whether a mulivalued expression that appears multiple times has to use the same value each time., and just canceling them where appropriate avoids that question.
So you're solving for both 'w' and 'z'? Crazy.
I get the allure of a power that doubles, but why drag it out with all the periodicity manipulations? Do the multiples of two pi enhance the allure or burden it with overdone pedantry? The principal branch ought to suffice.
I don't know why stupid me thought it was lambertW function.
It would have been if you swap z and w in the LHS. You are not stupid, you are a pattern recognizer.
Great comment! 😍
I pretty much got the same answer - I'm just missing the 2*pi*n*i part.
It's a shame you have to follow the rules, because your first answer is pretty nice😂
w^z-2w=0
w(w^(z-1)-2)=0
w=0
w^(z-1)-2=0
w^(z-1)=2
(z-1)*lnw=ln2
z-1=ln2/lnw
z=ln2/lnw +1=ln(2w)/lnw😮
ORV??????????
@@JuanMartinez-ge7nl Omniscient reader's viewpoint!