Question

Log2+16log16/15+12log25/24+7log81/80

Answer 1

 log2 + 16log16 - 16log15 + 12log25 - 12log24 +7log81 - 7log80 
= log2 + 16(4log2) - 16(log3 + log5) + 12(2log5) -12(3log2 +log3) + 7(4log3) - 7(log5 + 4log2) 
= log2*(1+64 -36-28) +log3*(-16 -12+28) + log5(-16+24-7) 
=log2* 1 + log3*(0) + log5*(1) 
= log2+log5 
= log10 
=1.
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Answer 2

$log2 + 16log \frac{16}{15} +12log \frac{25}{24} +log\frac{81}{80}$

$log[2( \frac{16}{15} )^{16} ( \frac{25}{24} )^{12} (\frac{80}{81} )^{7}]$

$log[ \frac{2^{65}5^{24}3^{28}}{3^{28}2^{64} 5^{23} } ]$

$log10 = 1$