Question

Se log a= 8 log b= 6 log c= 2 resolva:

log √ab÷c

log √a÷b

log 3√b÷c

Answer 1

$log \sqrt{ \frac{ab}{c}} =log( \frac{ab}{c})^{1/2}=loga^{1/2}+logb^{1/2}-logc^{1/2}= \\ \\ \frac{1}{2}loga+ \frac{1}{2}logb- \frac{1}{2}logc \\ \\ \frac{8}{2}+ \frac{6}{2}- \frac{2}{2}=4+3-1=6$

$log \sqrt{ \frac{a}{b} } =log( \frac{a}{b})^{1/2}= \frac{1}{2}loga- \frac{1}{2}logb= \frac{8}{2}- \frac{6}{2}=4-3=1$

$3log( \frac{b}{c})^{1/2}= \frac{3}{2}logb- \frac{3}{2}logc= \frac{3.6}{2}- \frac{3.2}{2}=9-3=6$