Where to find a ebony bow in skyrim

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  http://gameslikeskyrim.com/skyrim-best-bow-list-of-the-best-bows-in-skyrim/
This bow may appear to be just another above average bow, but it is actually one of the most powerful bows in the game if you factor in the special effects. The base damage of 14 is good, but it is particularly valuable in the hands of an aspiring mage (or a character who frequently does battle with magicka characters)

Ebony Bow (Skyrim) - The Elder Scrolls Wiki

  http://elderscrolls.wikia.com/wiki/Ebony_Bow_(Skyrim)
It is made at a blacksmith's forge with the following components: 3 x Ebony Ingots It can be upgraded with an Ebony Ingot at a grindstone and also benefits from the Ebony Smithing perk, which doubles the improvement