Question

prove that 7 log10\9 - 2 log25 \24 + 3 log81 \80 = log2

Answer 1

LHS = 7 log(10/9) - 2log(25/24) + 3 log( 81/80)

= 7log{(2*5)/3²} - 2log{5²/ (2^3 *3)} + 3log{(3^4/(2^4*5)}

= 7( log 2 + log5 - 2log3) -2 (2log 5- 3log2-log3) + 3(4log3 - 4log2–log5)

= 7log2+ 7log5- 14log3 - 4log5 + 6log2 + 2log 3 + 12log3 - 12log2 - 3log 5..

= (7log2+ 6log2 -12log2 ) + (7log5 - 4log5–3log5)

= 13log2 - 12 log2 + 3log5 - 3log5

= log2 = RHS

So, LHS = RHS

Answer 2

Answer:

In attachment I have answered this question.