# Minimum value?

Algebra Level 4

If $$\log_4 (x+2y)+ \log_4 (x-2y) = 1$$, and the minimum value of $$|x|-|y|$$ is $$k$$, then find $$\lceil k \rceil$$.

Notation: $$\lceil \cdot \rceil$$ denotes the ceiling function.

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