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can normal tetration be defined as a limit of product tetration?

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can normal tetration be defined as a limit of product tetration?
Alex Zuma 2025 Offline
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#1
52 minutes ago (This post was last modified: 49 minutes ago by Alex Zuma 2025.)
it is hypothesized that if you take infinitely many arbitrary base logarithms of product tetration with the same base, you will eventually get normal tetration with the base you chose.
but is it really true? someone please let me know.
here's an image to make things clearer:
   
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