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mathmath333
 one year ago
soft question
mathmath333
 one year ago
soft question

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0if \(y=\log x,\ \{x,y\}\in \mathbb{R}\) can \(x\) be \(0\) or \(x<0\)

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1no! e^y=0???? can you find such number that goes with that

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1or any base actually b^a=0!!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2x can be only >0

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0and what about \(x<0\)

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1the same reason goes for x<0 e^y is always positive thus log x for x>0

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2the logarithm function is defined for positive numbers only, so x can not be < 0

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1this restrictions are there for the bond to exp

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0by the way is there a logarithm for negative numbers

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1there is only one possibility that a power result in zero that is the case 0^0 but that is a calculus problem hehe

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1it is not quite zero but not 1 either!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2no, there is not a logarithm of negative number

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1you mean log base negative ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0and what about complex numbers

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0i mean where x can be taken negative

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1no cannot x>0 always

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2yes! I think that the logarithm of a complex number is defined

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1in complex theory, yes there are some stuff of that sort:) i didn't take complex analysis yet but i do believe they do some kind of tricks around that

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1but logs take multiple values in some way! if we allow it to be complex function

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2if we define a complex number like this: \[\Large z = \rho {e^{i\theta }}\] then the logarithmic function is: \[\Large f\left( z \right) = \ln z = \ln \rho + i\theta \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2where the subsequent additional contition holds: \[\Large 0 \leqslant \theta < 2\pi \]

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1it is a whole other interesting place :) complex numbers tend to solve such problem with some good tricks

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2that's right! @xapproachesinfinity
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