Restrictions with Exponents

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How many positive integers x x are there that satisfy 9 x < 6 75 9^x<6^{75} and x ! > 1 0 9 x!>10^9 ?


The answer is 49.

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1 solution

Budi Utomo
Dec 25, 2013

{x}_max in 9^{x}\<6^{75} --> {x}=61 and {x}_min in {x!}\<10^{9} --> {x}=13. So, {x} are {13} {-} {61} = {49}. (Answered)

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