Question

23 log 10/9 - 6 log 25/24 + 10 log 81/80
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Answer 1

23log(10/9) - 6log(25/24) + 10log( 81/80)

= 23log{(2*5)/3²} - 6log{5²/ (2^3 *3)} + 10log{(3^4/(2^4*5)}

= 23( log 2 + log5 - 2log3) -6(2log 5- 3log2-log3) + 10(4log3 - 4log2–log5)

= 23log2+ 23log5- 46log3 - 12log5 + 18log2 + 6log 3 + 40log3 - 40log2 - 10log 5..

= (23log2+ 18log2 -40log2 ) + (23log5 - 12log5–10log5) =log2+log5

=log(2×5)

=log10

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