Log2+16 log16/15 + 12 log 25/24 +7 log 81/80

Asked by rgkgmu | 8th Aug, 2015, 06:17: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e x p r e s s i o n colon log 2 plus 16 log 16 over 15 plus 12 log 25 over 24 plus 7 log 81 over 80 W e space k n o w space t h a t space n log a equals log a to the power of n T h u s comma space w e space h a v e comma l o g 2 plus 16 l o g 16 over 15 plus 12 l o g 25 over 24 plus 7 l o g 81 over 80 equals l o g 2 plus l o g open parentheses 16 over 15 close parentheses to the power of 16 plus l o g open parentheses 25 over 24 close parentheses to the power of 12 plus l o g open parentheses 81 over 80 close parentheses to the power of 7 equals l o g open square brackets 2 cross times open parentheses 16 over 15 close parentheses to the power of 16 cross times open parentheses 25 over 24 close parentheses to the power of 12 cross times open parentheses 81 over 80 close parentheses to the power of 7 close square brackets space space space space space space space space space open square brackets because log A plus log B plus log C equals log A B C close square brackets equals l o g open square brackets 2 cross times open parentheses fraction numerator 2 to the power of 4 over denominator 5 cross times 3 end fraction close parentheses to the power of 16 cross times open parentheses fraction numerator 5 squared over denominator 2 cubed cross times 3 end fraction close parentheses to the power of 12 cross times open parentheses fraction numerator 3 to the power of 4 over denominator 2 to the power of 4 cross times 5 end fraction close parentheses to the power of 7 close square brackets space equals l o g open square brackets 2 cross times fraction numerator 2 to the power of 64 over denominator 5 to the power of 16 cross times 3 to the power of 16 end fraction cross times fraction numerator 5 to the power of 24 over denominator 2 to the power of 36 cross times 3 to the power of 12 end fraction cross times fraction numerator 3 to the power of 28 over denominator 2 to the power of 28 cross times 5 to the power of 7 end fraction close square brackets space equals l o g open square brackets 2 cross times fraction numerator 2 to the power of 64 cross times 5 to the power of 24 cross times 3 to the power of 28 over denominator 2 to the power of 64 cross times 3 to the power of 28 cross times 5 to the power of 23 end fraction close square brackets space equals l o g open square brackets 2 cross times 5 close square brackets space equals l o g open square brackets 10 close square brackets space equals 1

Answered by Vimala Ramamurthy | 8th Aug, 2015, 08:11: PM