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## Main Question or Discussion Point

$$ƒ = b^n$$

$$ b,n,I ∈ ℤ $$

Condition: Upon choosing a base value [itex]b[/itex]..

$$ n | b^n ≤ I $$

(n is determined based off the value of [itex]b[/itex] to yield the highest ƒ without going over [itex]I[/itex])

$$1<b<L , L<<I$$

where [itex]I[/itex] is some large number, and [itex]L[/itex] is also sufficiently large such that we want to avoid going through each base integer via trial and error....

How might I determine the base value that yields a value [itex]ƒ[/itex] that is closest to [itex]I[/itex]?

$$ b,n,I ∈ ℤ $$

Condition: Upon choosing a base value [itex]b[/itex]..

$$ n | b^n ≤ I $$

(n is determined based off the value of [itex]b[/itex] to yield the highest ƒ without going over [itex]I[/itex])

$$1<b<L , L<<I$$

where [itex]I[/itex] is some large number, and [itex]L[/itex] is also sufficiently large such that we want to avoid going through each base integer via trial and error....

How might I determine the base value that yields a value [itex]ƒ[/itex] that is closest to [itex]I[/itex]?