Using solve command for specific pair of equations in Maple produces no result, but a simple algebraic change produces a result, why?

Question

Say I have the following two equations:

$$2000 = k \ln {\frac{t+1}{t}}$$ $$2000 = k \ln {\frac{t+3}{t+1}}$$

The solution for $t$ is $t=1$, which is easily obtained equating the two equations and exponentiating both sides.

In Maple, this is:

e1 := 2000 = k*ln((t + 1)/t)
e2 := 2000 = k*ln((t + 3)/(t + 1))
solve({ e1, e2 }, { t })

The $solve$ command produces no result above. If instead I do

e3 := k*ln((t + 1)/t) = k*ln((t + 3)/(t + 1))
solve(e3, t)

I obtain the correct answer $t=1$.

Why doesn't the solve command work when $e1$ and $e2$ are considered a system of two equations?

Answer 1

e1 := 2000 = k*ln((t + 1)/t)
e2 := 2000 = k*ln((t + 3)/(t + 1))
solve({ e1, e2 }, { t , k})

works fine, and returns the solution. You asked for maple to solve the system for t but to keep k arbitrary -- there is indeed no solution then.