UnkleRhaukus
  • UnkleRhaukus
\[100^x=0^+\]
Mathematics
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chestercat
  • chestercat
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ganeshie8
  • ganeshie8
\[100^x=0^+ ~~\iff~~x=\log_{100}0^{+}=-\infty\]
UnkleRhaukus
  • UnkleRhaukus
\[x = \lim_{y\to-\infty}y\]
ganeshie8
  • ganeshie8
i think we can avoid the limits by moving to extended reals

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UnkleRhaukus
  • UnkleRhaukus
but \[100^x=0 \quad\implies\quad x=-\infty\]
ganeshie8
  • ganeshie8
Nope, I see what you did there. identically equal to 0 and tens to 0 from positive side are two different things
ganeshie8
  • ganeshie8
*tends
UnkleRhaukus
  • UnkleRhaukus
right
ganeshie8
  • ganeshie8
At any rate below should be fine \[100^x= 0^{+}\quad\implies\quad x=-\infty\] if \(0^{+}\) is defined as getting close to 0 from right hand side, but honestly i never worked wid these operators... so i think "+ on top right corner" operation needs to be defined first.
UnkleRhaukus
  • UnkleRhaukus
\[100^x= 0^{+}\quad\implies\quad x=-\infty^+\]
ganeshie8
  • ganeshie8
what does that even mean xD

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