Question

Prove that log 2+6 log 16/15 +12 log 25/24+7log 81/80=1

Answer 1

Answer:

Step-by-step explanation:

log 2+ 6 log 16/15 +  12 log 25/24 + 7log 81/80=1

LHS=log 2+16 log 16/15 +12 log 25/24+7log 81/80

=log 2 +16 log  2^4 /(3*5) +12 log 5²/2³*3 + 7 log 3^4/2^4 * 5

=log 2 +16*(4log2-log3-log5)+ 12*(2 log 5-3log2-log 3)+7*( 4log3-4 log 2-log5)

=log 2+64log2-16log3-16log5 +24log 5-36log2-12log3+28log3-28 log2-7log5

= log2 +log 5

==log 2+log5)

=log { 2*5}

=log 10

=1=RHS