If I use Lazav, the Multifarious's ability, targeting Mikaeus, the Lunarch which is in my graveyard, what will happen? The X in Lazav's activated ability is a different X from the one in Mikaeus's mana cost. However, in this case, the value of X in Mikaeus' mana cost is taken to be 0 in determining the cost of Lazav's activated ability. Will Lazav, the Multifarious die immediately?
In general, after Lazav becomes a copy of Mikaeus, Lazav will be 0/0 and go to the graveyard as a state-based action (unless something is raising Lazav's toughness to 1 or greater, such as if Lazav already has +1/+1 counters on it [C.R. 122.1a, 613.4c, 613.1a, 613.1g]) (C.R. 704.5f). Lazav won't be given +1/+1 counters when it becomes a copy of Mikaeus this way, since it's not entering the battlefield and because in this situation, "Mikaeus, the Lunarch enters the battlefield with X +1/+1 counters on it" is not an "ability [that] defines a value of X" (C.R. 107.3i).
A permanent, already on the battlefield, whose characteristics have merely changed (whether by becoming a copy of another object or otherwise) doesn't "reenter the battlefield" this way (C.R. 110.1; for copy effects, compare C.R. 706.4, which covers this scenario, with C.R. 706.5, which covers such cards as Clone). In general, an object enters the battlefield if it formerly wasn't on the battlefield but is now there. See also this thread and this thread.
Even if Lazav were to re-enter the battlefield by becoming a copy of Mikaeus, it would still be given no +1/+1 counters this way, since the X on Mikaeus's first ability would be 0 in this situation (C.R. 107.3e, 107.2; see also this thread).
in this case, the value of X in Mikaeus' mana cost is taken to be 0 in determining the cost of Lazav's activated ability.
This is misleading. There are two 'X' in this situation (one on Mikaeus and one on Lazav) and they have different values.
While it's in the graveyard, Mikaeus' converted mana cost is one (the zero value of its X and the white mana), therefore Lazav's ability will cost one mana and its X is 1.
A permanent, already on the battlefield, whose characteristics have merely changed (whether by becoming a copy of another object or otherwise) doesn't "reenter the battlefield" this way (C.R. 110.1; for copy effects, compare C.R. 706.4, which covers this scenario, with C.R. 706.5, which covers such cards as Clone). In general, an object enters the battlefield if it formerly wasn't on the battlefield but is now there. See also this thread and this thread.
Even if Lazav were to re-enter the battlefield by becoming a copy of Mikaeus, it would still be given no +1/+1 counters this way, since the X on Mikaeus's first ability would be 0 in this situation (C.R. 107.3e, 107.2; see also this thread).
While it's in the graveyard, Mikaeus' converted mana cost is one (the zero value of its X and the white mana), therefore Lazav's ability will cost one mana and its X is 1.
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