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

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rosey-girl | Student, Grade 12 | (Level 1) Valedictorian

Posted April 15, 2013 at 11:15 PM via web

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Expand each logarithm:

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

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mjripalda | High School Teacher | (Level 1) Senior Educator

Posted April 16, 2013 at 12:11 AM (Answer #1)

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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` .

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oldnick | (Level 1) Valedictorian

Posted April 16, 2013 at 12:12 AM (Answer #2)

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`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)`

 

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