- #1
bins4wins
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Prove that if ##m > 1## such that there exists a ##c > 1## that satisfies
$$cm < m^c$$
then for any ##k > c##
$$km < m^k$$
holds. Prove this without using logarithms or exponents or calculus. Basically using the properties of real numbers to prove this.
One attempt I have tried, but didn't seem to work, was trying to show this inequality using integers, then moving on to rationals, and ultimately real numbers.
$$cm < m^c$$
then for any ##k > c##
$$km < m^k$$
holds. Prove this without using logarithms or exponents or calculus. Basically using the properties of real numbers to prove this.
One attempt I have tried, but didn't seem to work, was trying to show this inequality using integers, then moving on to rationals, and ultimately real numbers.
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