Question

Log1/2 28? What is it?

Answer 1

$\log_a(b\cdot c)=\log_ab+\log_ac\\\\\log_ab^c=c\cdot\log_ab\\\\\log_aa=1\\--------------------\\\log_\frac{1}{2}28=\log_\frac{1}{2}(4\cdot7)=\log_\frac{1}{2}4+\log_\frac{1}{2}7=\log_\frac{1}{2}2^2+\log_\frac{1}{2}7\\\\=2\log_\frac{1}{2}2+\log_\frac{1}{2}7=\boxed{2+\log_\frac{1}{2}7}$


$\log_ab=\frac{\log_cb}{\log_ca}\\-------------------------\\\log_\frac{1}{2}7=\frac{\log\frac{1}{2}}{\log7}\approx\frac{-0.6931}{1.9459}\approx-0.3562\\\\therefore\\\\\boxed{\log_\frac{1}{2}28\approx2+(-0.3562)=1.6438}$