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## Main Question or Discussion Point

I can't prove it and I've got it by some intuition because not many properties of superlogarithms are known. I don't think anyone can prove it but is there some way to at least check if it is correct.

The limit is:

$$\lim_{h\rightarrow0}slog_{[log_xx+h]}[log_{f(x)}f(x+h)]$$

where ##slog## is the super-logarithm.

What I need to check is if this limit equals:

$$log_{log_xf(x)}[\frac{d(f(x))}{dx}\frac{x}{y}]$$

for any function ##f(x)##. It's true when ##f(x)=x^n##. But is there some way to check if it's right or wrong for other functions?

The limit is:

$$\lim_{h\rightarrow0}slog_{[log_xx+h]}[log_{f(x)}f(x+h)]$$

where ##slog## is the super-logarithm.

What I need to check is if this limit equals:

$$log_{log_xf(x)}[\frac{d(f(x))}{dx}\frac{x}{y}]$$

for any function ##f(x)##. It's true when ##f(x)=x^n##. But is there some way to check if it's right or wrong for other functions?

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