3log₆ - 2log ( ) 64 +4log₀,₂

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To simplify this expression, we need to use logarithmic properties to combine and simplify the terms.

Starting with the terms:

Let's simplify one by one:

This can be simplified as log₆(6^3) = log₆(216).

This can be simplified as log(64) = log₆(2^6) = 6log₆(2).

This can be simplified as log₀,₂ = logx(x) where x=2, which is equal to 1.

Bringing all the simplified terms together:

log₆(216) + 6log₆(2) + 4(1)

Now we can combine the terms:

log₆(216) + 6log₆(2) + 4
= log₆(216) + log₆(2^6) + 4
= log₆(216*2^6) + 4
= log₆(13824) + 4

Therefore, the simplified form of the expression is log₆(13824) + 4.