Two translations of Isa 40:2 are,
Speak ye comfortably to Jerusalem, and cry unto her, that her warfare is accomplished, that her iniquity is pardoned: for she hath received of the Lord’s hand double for all her sins. Isa 40:2 (KJV)
Speak tenderly to Jerusalem, and cry to her that she has served her term, that her penalty is paid, that she has received from the Lord’s hand double for all her sins. Isa 40:2 (NRSV)
The KJV represents the more common translation of the English versions, ‘warfare is ended’, while the NRSV represents the more common view of recent commentaries on Isaiah, which offer something like the idea of ‘her hard service has ended’. The problem with both translations is that they do not represent majority usage of the Hebrew words involved, which would otherwise suggest a translation of ‘her host is full’. It is interesting therefore to observe that the Christian translation of the English versions differs from Jewish translation and that of the commentary of A. J. Rosenberg, who translates the Hebrew as “she has become full from her host”.[1] It is not difficult to see how this translation fits a pre-exilic setting in the lifetime of Isaiah of Jerusalem, but modern Christian commentaries are beholden to the post-exilic reading of Isa 40:1-11 set by the German Higher Critics and direct the reader to the idea of a term of service in exile as being over.
The second thing to note in this verse is the obscure reference to a ‘double’ or ‘doubling’. Is this a reference to a double blessing or a double punishment? The key to ‘double/doubling’ is Isa 51:19,
These two things are come unto thee; who shall be sorry for thee? Desolation, and destruction, and the famine, and the sword: by whom shall I comfort thee? Isa 51:19 (KJV)
The word for ‘two’ here is different but the verse mentions two pairs (not just two things), which gives us the exegesis of the ‘doubling’ of Isa 40:2. These terms (‘destruction’ and ‘desolation’; ‘famine’ and ‘sword’) have a ready reference in the recent Assyrian invasion and its aftermath. The rhetorical question, ‘By whom shall I comfort you’ picks up on the ‘Comfort ye, comfort ye’ of Isa 40:1 which is also an introductory pair. The logic here is that the two things of her host being full and her iniquity being accepted corresponds to (compensates for) the ‘double’ punishment she received.
[1] A. J. Rosenberg, Isaiah (Judaica Series; 2 vols; New York: Judaica Press, 1987), 313.