Question

Ajuda com Logaritmo!

Answer 1

a)

$log\ \sqrt{32_,4} = log\ \sqrt{\frac{162}{5}} = log\ \frac{162}{5}^\frac{1}{2}\\\\ \frac{1}{2}\ log\ \frac{162}{5}\\\\ \frac{1}{2}(log\ 162-log\ 5)\\\\ \frac{1}{2}(log\ 2*3^4-(log\ \frac{10}{2}))\\\\ \frac{1}{2}(log\ 2+4\ log\ 3-(log\ 10-log\ 2))\\\\\ \frac{1}{2}(0,3+4*0,48-(1-0,3))\\\\ \frac{1}{2}(0,3+1,92-0,7)\\\\ \frac{1}{2}(1,52)\\\\ \boxed{log\ \sqrt{32_,4} = 0,76}$

b) 

$log\ 45=log\ 3^2*5\\\\ log\ 45=2\ log\ 3+log\ 5\\\\ log\ 45=2*0,48+0,7\\\\ log\ 45=0,96+0,7\\\\ \boxed{log\ 45=1,66}$

c) 

$log\ 2_,4 = log\ \frac{24}{10}\\\\ log\ 2_,4=log\ 24-log\ 10\\\\ log\ 2_,4=log\ 2^3*3-log\ 10\\\\ log\ 2_,4=3\ log\ 2+log\ 3-log\ 10\\\\ log\ 2_,4=0,9+0,48-1\\\\ \boxed{log\ 2_,4=0,38}$

d)

$log\ 144 = log\ 12^2\\\\ log\ 144=2\ log\ 12\\\\ log\ 144=2 (log2^2*3)\\\\ log\ 144=2(2\ log\ 2+log\ 3)\\\\ log\ 144=2(0,6+0,48)\\\\ log\ 144=2(1,08)\\\\ \boxed{log\ 144=2,16}$