Closed-form of an infinite sum

Dear All,

I would like to find (if it exists) a closed-form expression for the
following expression:

sum( (a^(t-1)) * ln(x_t) ) with t (discrete) from 1 to +oo,

and x_(t+1) = a * x_t, 0 < a < 1, x_0 > 0.

Any suggestions?

Thanks in advance,

Paul

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