Question

Find the answer for this
question

Answer 1

log2 + 16log(16/15) + 12log(25/24) + 7log(81/80)

=log2 + 16( log16 -log15 ) +12( log25 -log24) +7( log81 -log80)

=log2 + 16(log2⁴ -log3×5) + 12(log5² -log2³×3) +7(log3⁴ -log2⁴ ×5)

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

= ( 1 + 16× 4 -12×3 -7×4) log2 + ( -16×1 -12×1 +7 ×4) log3 + ( -16×1 +12×2 -7×1) log5

=( 1 + 64 -36 -28)log2 + ( -16 -12 +28)log3 + ( -16+24 -7)log5

= log2 + 0× log3 +log5


= log2 + log5

= log10

= 1 ( answer )