UnkleRhaukus one year ago $100^x=0^+$

1. ganeshie8

$100^x=0^+ ~~\iff~~x=\log_{100}0^{+}=-\infty$

2. UnkleRhaukus

$x = \lim_{y\to-\infty}y$

3. ganeshie8

i think we can avoid the limits by moving to extended reals

4. UnkleRhaukus

but $100^x=0 \quad\implies\quad x=-\infty$

5. ganeshie8

Nope, I see what you did there. identically equal to 0 and tens to 0 from positive side are two different things

6. ganeshie8

*tends

7. UnkleRhaukus

right

8. 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.

9. UnkleRhaukus

$100^x= 0^{+}\quad\implies\quad x=-\infty^+$

10. ganeshie8

what does that even mean xD