Solve command with assumptions

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Hi,

I'm trying to solve the following inequality $$ ce ^{-kt} - 1 < 0 $$ where, c and k are positive real numbers.

Expected result is $$ t < -\frac{1}{k} \ln({\frac{1}{c})} $$

But sage is returning $$ -c + e^{kt} > 0 $$

Code is as follows:

c, k = var('c k')
assume(c > 0, k > 0)
eq3 = (c*e^(-k*t)) -1 < 0
solve(eq3, t)

Is there something wrong with my code? Thanks in advance.