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

tharun
21 Points
6 years ago
(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.
Captain Cool
12 Points
6 years ago
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
12 Points
6 years ago
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