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If $c=a+b$, then $a=c-b$ and $b=c-a$. If $c=a\times b$, then $a=\frac{c}{b}$ and $b=\frac{c}{a}$. If $c=a^b$, then $a = \sqrt [b]{c} =c^{\frac{1}{b}}$ and $b=log_ac$.

What are the analogous inverse operations for $^ba=c$ and how are they computed?

I researched this a bit, but couldn't find any appropriate notation.

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The inverse of $^ba = c$

$a = \sqrt [b]{c}_s$ ,for $b \in \Bbb N$

Where $\sqrt {(..)}_s$ is Super square root

And $b=slog_a(c)$

Where $Slog(..)$ is Super logarithm

Be careful that $^b(^{1/b}a) \not = a$

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