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_(1)/(2)28=\log_(1)/(2)(4\cdot7)=\log_(1)/(2)4+\log_(1)/(2)7=\log_(1)/(2)2^2+\log_(1)/(2)7\\\\=2\log_(1)/(2)2+\log_(1)/(2)7=\boxed{2+\log_(1)/(2)7}`



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