Dividing 39 by 26 produces a answer of 1.5; i.e., the rear wheel will turn 1.5 times for each time the pedals go around.

So you want to know what number, when divided into 34 (i.e., your new chainring size) produces 1.5, so we get:
(34 / X) = (39 / 26)
(34 / X) = 1.5
... multiply both sides by X and you get:
34 * X / X = 1.5 * X
... the X's cancel out, so you get:
34 = 1.5 * X
... divide both sides by 1.5, and you get:
34 / 1.5 = X

Whip out your calculator, and you get 22.6. So there's no exact match for a 39x26 in the compact world, but a 34x23 is so close as to be unnoticeably different.