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Log3-log2⁸÷log3⁹
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Log3-log2⁸÷log3⁹

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challegoddeythis
Asked by challegoddeythisrep:3
Ghana
22 April 2021

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peter
Peter answeredrep:1.8K
University of Lagos Nigeria
22 April 2021
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Log3 - log28 ÷ log39

From rules of logarithm, 

-log(x) = log(1/x)

= Log3 + log(1/28) ÷ log(39)

= Log3 + log(1/28 ÷ 39)

= Log3 + log(2-8 ÷ 39)

From rules of logarithm, log(x ÷ y) = log(x) - log(y)

Thus,

= log3 + log2-8 - log39

= log3 - 8log2 - 9log3

= - 8log2 - 8log3

= 8log(1/2) + 8log(1/3)

From rules of logarithm, 

alog(x) + alog(y) = alog(x × y)

= 8log(1/2 × 1/3)

= 8log(1/6)

= log ((1/6)8)

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dp
adeb
it can also be simplified to -log(6^8)
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