Find log2448 in terms of a if log1236 =a

Asked by Anil | 5th May, 2017, 12:36: PM

Expert Answer:

begin mathsize 16px style log subscript 24 48
equals log subscript 24 open parentheses 24 cross times 2 close parentheses
equals log subscript 24 24 plus log subscript 24 2
equals 1 plus fraction numerator 1 over denominator log subscript 2 24 end fraction
equals 1 plus fraction numerator 1 over denominator log subscript 2 open parentheses 8 cross times 3 close parentheses end fraction
equals 1 plus fraction numerator 1 over denominator log subscript 2 8 plus log subscript 2 3 end fraction
equals 1 plus fraction numerator 1 over denominator log subscript 2 2 cubed plus log subscript 2 3 end fraction
equals 1 plus fraction numerator 1 over denominator 3 log subscript 2 2 plus log subscript 2 3 end fraction
equals 1 plus fraction numerator 1 over denominator 3 plus log subscript 2 3 end fraction................ left parenthesis straight i right parenthesis
Given space
log subscript 12 36 equals straight a
log 12 6 squared equals straight a
2 log subscript 12 6 equals straight a
log subscript 12 6 equals straight a over 2
fraction numerator 1 over denominator log subscript 6 12 end fraction equals straight a over 2
fraction numerator 1 over denominator log subscript 6 open parentheses 6 cross times 2 close parentheses end fraction equals straight a over 2
fraction numerator 1 over denominator 1 plus log subscript 6 2 end fraction equals straight a over 2
simplifying space in space such space straight a space way space till space you space get space
log subscript 2 3 equals fraction numerator 2 straight a minus 2 over denominator 2 minus straight a end fraction
Put space this space in thin space left parenthesis straight i right parenthesis
log subscript 24 48 equals fraction numerator 2 open parentheses 3 minus straight a close parentheses over denominator 4 minus straight a end fraction
end style

Answered by Sneha shidid | 5th May, 2017, 05:03: PM