Question

4º)Dados: log2 ≈ 0,3; log3 ≈ 0,5 e log7 ≈ 0,8, calcule:
a) log30       b)
log16/18           d)
log1,25       e) log0,45  

Answer 1

$log\ 30 = log\ 2\cdot3\cdot5\\\\\\ log\ 2+log\ 3+log\ 5\\\\\ log\ 5 = log\ \frac{10}{2}\\\\ log\ 5 = 1-0,3\\\\ log\ 5 = 0,7\\\\\ log\ 30 = 0,3+0,5+0,7\\\\\ \boxed{log\ 30 = 1,5}$

$log\ \frac{16}{18} = log\ \frac{2^4}{2\cdot3^2} = 4\ log\ 2-(log\ 2+2\ log\ 3)\\\\\ log\ \frac{16}{18} = 4\cdot0,3-(0,3+2\cdot0,5)\\\\\ log\ \frac{16}{18} = 1,2-(0,3+1,0)\\\\\ \boxed{log\ \frac{16}{18} = -0,1}$

$log\ 1,25 = log\ \frac{125}{100} = log\ \frac{5^3}{10^2}\\\\ log\ 1,25 = 3\ log\ 5-2\ log\ 10\\\\\ log\ 1,25 = 3\cdot0,7-2\cdot1\\\\ log\ 1,25 = 2,1-2\\\\\ \boxed{log\ 1,25 = 0,1}$

$log\ 0,45 = log\ \frac{45}{100} = log\ \frac{3^2\cdot5}{10^2}\\\\\ log\ 0,45 = 2\ log\ 3+log\ 5-2\ log\ 10\\\\\ log\ 0,45 = 2\cdot0,5+0,7-2\cdot1\\\\\ log\ 0,45 = 1+0,7-2,0\\\\\ log\ 0,45 = 1,7-2,0\\\\\ \boxed{log\ 0,45=-0,3}$