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) + = log₆(216) + log₆(2^6) + = log₆(216*2^6) + = log₆(13824) + 4
Therefore, the simplified form of the expression is log₆(13824) + 4.
To simplify this expression, we need to use logarithmic properties to combine and simplify the terms.
Starting with the terms:
3log₆-2log( ) 64+4log₀,₂Let's simplify one by one:
3log₆This can be simplified as log₆(6^3) = log₆(216).
-2log( ) 64This can be simplified as log(64) = log₆(2^6) = 6log₆(2).
+4log₀,₂This 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) +
= log₆(216) + log₆(2^6) +
= log₆(216*2^6) +
= log₆(13824) + 4
Therefore, the simplified form of the expression is log₆(13824) + 4.