Question

Se log 2 = 0, 30, log 3 = 0, 47 e log 5 = 0, 69, calcule: a) log 20 b) log √6

Answer 1

a)
$\displaystyle \log20=\log(2^2\cdot5)=\log2^2+\log5=2\cdot\log2+\log5=2(0,3)+0,69\\ \log20=0,6+0,69=\boxed{1,29}$

b)
$\displaystyle \log\sqrt6=\log6^{\frac{1}{2}}=\frac{1}{2}\log6=\frac{1}{2}\log(3\cdot2)=\frac{1}{2}\log3+\frac{1}{2}\log2=\frac{0,47+0,3}{2}\\\\ \log\sqrt6=\frac{0,77}{2}=\boxed{0,385}$