show all the steps.

Asked by akash kumar | 11th Jul, 2017, 04:58: PM

Expert Answer:

begin mathsize 16px style log space 5 plus 16 log open parentheses 625 over 6 close parentheses plus 12 log open parentheses 4 over 375 close parentheses plus 7 log open parentheses 81 over 1250 close parentheses
equals log space 5 plus log open parentheses 625 over 6 close parentheses to the power of 16 plus log open parentheses 4 over 375 close parentheses to the power of 12 plus log open parentheses 81 over 1250 close parentheses to the power of 7
equals log space 5 plus log open parentheses fraction numerator 5 to the power of 4 over denominator 2 cross times 3 end fraction close parentheses to the power of 16 plus log open parentheses fraction numerator 2 squared over denominator 25 cross times 15 end fraction close parentheses to the power of 12 plus log open parentheses fraction numerator 3 to the power of 4 over denominator 625 cross times 2 end fraction close parentheses to the power of 7
equals log space 5 plus log open parentheses fraction numerator 5 to the power of 4 over denominator 2 cross times 3 end fraction close parentheses to the power of 16 plus log open parentheses fraction numerator 2 squared over denominator 5 squared cross times 5 cross times 3 end fraction close parentheses to the power of 12 plus log open parentheses fraction numerator 3 to the power of 4 over denominator 5 to the power of 4 cross times 2 end fraction close parentheses to the power of 7
equals log space 5 plus log open parentheses fraction numerator 5 to the power of 4 cross times 16 end exponent over denominator 2 to the power of 16 cross times 3 to the power of 16 end fraction close parentheses plus log open parentheses fraction numerator 2 to the power of 2 cross times 12 end exponent over denominator 5 to the power of 3 cross times 12 end exponent cross times 3 to the power of 12 end fraction close parentheses plus log open parentheses fraction numerator 3 to the power of 4 cross times 7 end exponent over denominator 5 to the power of 4 cross times 7 end exponent cross times 2 to the power of 7 end fraction close parentheses
equals log space open square brackets 5 cross times fraction numerator 5 to the power of 4 cross times 16 end exponent over denominator 2 to the power of 16 cross times 3 to the power of 16 end fraction cross times fraction numerator 2 to the power of 2 cross times 12 end exponent over denominator 5 to the power of 3 cross times 12 end exponent cross times 3 to the power of 12 end fraction cross times fraction numerator 3 to the power of 4 cross times 7 end exponent over denominator 5 to the power of 4 cross times 7 end exponent cross times 2 to the power of 7 end fraction close square brackets
equals log space open square brackets fraction numerator 5 cross times 5 to the power of 64 cross times 2 to the power of 24 cross times 3 to the power of 28 over denominator 2 to the power of 16 cross times 3 to the power of 16 cross times 5 to the power of 36 cross times 3 to the power of 12 cross times 5 to the power of 28 cross times 2 to the power of 7 end fraction close square brackets
equals log open square brackets fraction numerator 5 to the power of 65 cross times 2 to the power of 24 cross times 3 to the power of 28 over denominator 5 to the power of 64 cross times 2 to the power of 23 cross times 3 to the power of 28 end fraction close square brackets
equals log open square brackets 5 cross times 2 close square brackets
equals log space 10
equals 1 end style

Answered by Sneha shidid | 12th Jul, 2017, 09:05: AM