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## Main Question or Discussion Point

Say I have some exponential function floor(a^b)=x where a is irrational and b is an integer.

Is there a way to rewrite this as an exponential expression c^d without the need for a floor function where c is an integer?

For instance, floor(2.67^10) is 18,412, but I could also rewrite it as 2^14.1683587272239 or so but I only found that by arbitrarily choosing 2 as my base and solving for the exponent as log(18,412)/log(2). In this example, 2.67 is still rational but my point is that I want to change the base to an integer.

My question is whether or not I can rewrite the exponential given only floor(2.67^10) -- aka without using the "answer" of 18,412

Is there a way to rewrite this as an exponential expression c^d without the need for a floor function where c is an integer?

For instance, floor(2.67^10) is 18,412, but I could also rewrite it as 2^14.1683587272239 or so but I only found that by arbitrarily choosing 2 as my base and solving for the exponent as log(18,412)/log(2). In this example, 2.67 is still rational but my point is that I want to change the base to an integer.

My question is whether or not I can rewrite the exponential given only floor(2.67^10) -- aka without using the "answer" of 18,412