Solving an inequality over the natural numbers

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I am trying to find the smallest natural number k such that exp(k)+exp(-k)>193875.

Here's my code:

k = var('k')

assume(k, 'integer')

assume(k>0)

S = solve(exp(k)+exp(-k) > 193875, k)

S

Unfortunately, the output is [[e^(2k) - 193875e^k + 1 > 0]]

What can I do to solve this inequality?