FIND ? log 2 24 / log 96 2 – log 2 192 / log 12 2 = ….......

(log224/log962) – (log2192/log122)Due to base change rule, logab=1/logba.Therefore, we can use this rule to make the bases the same.=[(log224/(1/log296)] – [(log2192/(1/log212)] [base change rule]=(log224 x log296) – (log2192 x log212)Now, we can use the laws of logarithms that say that logam x logan = logamn=log2(24 x 96) – log2(192 x 12)Note:Let us not multiply the numbers.Now, we can use another laws of logarithms that say that logam / logan = logam/n=log2[(24 x 96) / (192 x 12)]=log21=0.

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9 grade maths> FIND ? log 2 24 / log 96 2 – log 2 192 / ...

FIND ?

log ₂24 / log ₉₆ 2 – log ₂192 / log ₁₂2 = ….......

Uyfgyjhfguh Ghfhfdh , 9 Years ago

Grade 9

3 Answers

tharun

(log₂24/log₉₆2) – (log₂192/log₁₂2)

Due to base change rule, log_ab=1/log_ba.

Therefore, we can use this rule to make the bases the same.

=[(log₂24/(1/log₂96)] – [(log₂192/(1/log₂12)] [base change rule]

=(log₂24 x log₂96) – (log₂192 x log₂12)

Now, we can use the laws of logarithms that say that log_am x log_an = log_amn

=log₂(24 x 96) – log₂(192 x 12)

Note:Let us not multiply the numbers.

Now, we can use another laws of logarithms that say that log_am / log_an = log_am/n

=log₂[(24 x 96) / (192 x 12)]

=log₂1

=0.

Last Activity: 8 Years ago

Captain Cool

We have to simplify log(2) 24 / log(96) 2 - log(2) 192 / log(12) 2log(2) 24 / log(96) 2 - log(2) 192 / log(12) 2use the property of logarithms: log(a) b = 1/log(b) a=> log(2) 24* log(2) 96 - log(2) 192 * log(2) 12=> log(2) 12*2 * log(2) 96 - log(2) 96*2 * log(2) 12=> [log(2) 12 + log(2) 2]* log(2) 96 - [log(2) 96 + log(2) 2]* log(2) 12=> log(2) 12 * log(2) 96 + log(2) 2 * log(2) 96 - log(2) 96 * log(2) 12 + log(2) 2* log(2) 12=> log(2) 12 * log(2) 96 + log(2) 96 - log(2) 96 * log(2) 12 - log(2) 12=> log(2) 96 - log(2) 12=> log(2) [ 96/12]=> log(2) 8=> 3The simplified form of log(2) 24 / log(96) 2 - log(2) 192 / log(12) 2 = 3

Last Activity: 8 Years ago

Captain Cool

rowseNotessearchSearch for any book or any questionHOMEWORK HELP > MATHReduce to the simplest form: log2(24)/log96(2) -log2(192)/log12(2)print Print document PDF list CiteEXPERT ANSWERSJUSTAGUIDE eNotes educator| CERTIFIED EDUCATORWe have to simplify log(2) 24 / log(96) 2 - log(2) 192 / log(12) 2log(2) 24 / log(96) 2 - log(2) 192 / log(12) 2use the property of logarithms: log(a) b = 1/log(b) a=> log(2) 24* log(2) 96 - log(2) 192 * log(2) 12=> log(2) 12*2 * log(2) 96 - log(2) 96*2 * log(2) 12=> [log(2) 12 + log(2) 2]* log(2) 96 - [log(2) 96 + log(2) 2]* log(2) 12=> log(2) 12 * log(2) 96 + log(2) 2 * log(2) 96 - log(2) 96 * log(2) 12 + log(2) 2* log(2) 12=> log(2) 12 * log(2) 96 + log(2) 96 - log(2) 96 * log(2) 12 - log(2) 12=> log(2) 96 - log(2) 12=> log(2) [ 96/12]=> log(2) 8=> 3The simplified form of log(2) 24 / log(96) 2 - log(2) 192 / log(12) 2 = 3

Last Activity: 8 Years ago