# Expand each logarithm: `log_8 (12^6 * 11)^4`

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`log_8(12^6*11)^4`

To expand, apply the power property of logarithm which is `log_b M^n = n log_b M` .

`=4log_8(12^6*11)`

Then,apply the product property which is `log_b(M*N)=log_bM+log_bN` .

`=4(log_8 12^6 + log_8 11)`

`=4log_8 12^6 + 4log_8 11`

And, apply the power property again for the first logarithm.

`=4*6log_8 12 + 4log_8 11`

`=24log_8 12 + 4log_8 11`

Hence, `log_8(12^6*11)^4=24log_8 12 + 4log_8 11` .

`log_8(12^6 .11)^4=4log_8(12^6 )(11)=`

`=4[6log_8(12)+log_8(11)]=`

`=4[18log_2(12)+3log_2(11)]=`

`=4[18log_2(4) + 18log_2(3)+3log_2(11)]=`

`=4[36+18log_2(3)+ 3log_2(11)]=`

`=144+72log_2(3)+12log_2(11)`