7log16/15 +5log25/24 +3log81/80 is equal to

Asked by Anil | 3rd May, 2017, 06:40: PM

Expert Answer:

begin mathsize 16px style 7 log 16 over 15 space plus 5 log 25 over 24 space plus 3 log 81 over 80
equals log open parentheses 16 over 15 close parentheses to the power of 7 plus log open parentheses 25 over 24 close parentheses to the power of 5 plus log open parentheses 81 over 80 close parentheses cubed
equals log open parentheses open parentheses 16 over 15 close parentheses to the power of 7 cross times open parentheses 25 over 24 close parentheses to the power of 5 cross times open parentheses 81 over 80 close parentheses cubed close parentheses
equals log open parentheses fraction numerator 2 to the power of 28 over denominator 3 to the power of 7 cross times 5 to the power of 7 end fraction cross times fraction numerator 5 to the power of 10 over denominator 2 to the power of 15 cross times 3 to the power of 5 end fraction cross times fraction numerator 3 to the power of 12 over denominator 2 to the power of 12 cross times 5 cubed end fraction close parentheses
equals log open parentheses 2 to the power of 28 minus 12 minus 15 end exponent cross times 5 to the power of 10 minus 7 minus 3 end exponent cross times 3 to the power of 12 minus 7 minus 5 end exponent close parentheses
equals log open parentheses 2 close parentheses end style

Answered by Sneha shidid | 4th May, 2017, 10:08: AM