Question

7 log $\frac{16}{15}$ + 5 log $\frac{25}{24}$ + 3 log $\frac{81}{80}$ = log2

Answer 1

$7log\frac{16}{15}+5log\frac{25}{24}+3log\frac{81}{80}=log2$

LHS

$7log\frac{16}{15}+5log\frac{25}{24}+3log\frac{81}{80}$

$=7[log16-log15]+5[log25-log24]+3[log81-log80]$

$=7[{log2}^4-log(3\times 5)]+5[{log5}^2-log(2^3\times 3)]+3[{log3}^4-log(2^4\times 5)]$

$=7[4log2-log3-log5]+5[2log5-3log2-log3]+3[4log3-4log2-log5]$

$=28log2-7log3-7log5+10log5-15log2-5log3+12log3-12log2-3log5$

$=log2(28-15-12)+log3(-7-5+12)+log5(-7+10-3)$

$=log2$

$=RHS$