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

Question

tharun · Answer

(log 2 24/log 96 2) – (log 2 192/log 12 2) Due to base change rule, log a b=1/log b a. Therefore, we can use this rule to make the bases the same. =[(log 2 24/(1/log 2 96)] – [(log 2 192/(1/log 2 12)] [base change rule] =(log 2 24 x log 2 96) – (log 2 192 x log 2 12) Now, we can use the laws of logarithms that say that log a m x log a n = log a mn =log 2 (24 x 96) – log 2 (192 x 12) Note:Let us not multiply the numbers. Now, we can use another laws of logarithms that say that log a m / log a n = log a m/n =log 2 [(24 x 96) / (192 x 12)] =log 2 1 =0.

Captain Cool · Answer

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

Captain Cool · Answer

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

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

FIND ?

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

3 Answers

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