Log_2⁡56 +2log_2⁡12-log_2⁡63

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First, we can simplify the terms using the properties of logarithms:

log₂56 = log₂(8 7) = log₂8 + log₂7 = 3 + log₂
log₂12 = log₂(4 3) = log₂4 + log₂3 = 2 + log₂
log₂63 = log₂(9 * 7) = log₂9 + log₂7 = 3 + log₂7

Now substitute these simplifications back into the original expression:

log₂56 + 2log₂12 - log₂63 = (3 + log₂7) + 2(2 + log₂3) - (3 + log₂7
= 3 + log₂7 + 4 + 2log₂3 - 3 - log₂
= 4 + 2log₂3

Therefore, log₂56 + 2log₂12 - log₂63 simplifies to 4 + 2log₂3.