Question

determine o valor de:


a)
$log(4) \frac{ \sqrt[3]{2} }{2}$
b)
$log_{0.2}0.04$
c)
$log_{0.04}0.2$
​

Answer 1

Resposta:

a)

$log_{4}( \frac{ \sqrt[3]{2} }{2} ) =x \\ log_{ {2}^{2} }( \frac{1}{2} \times \sqrt[3]{2} ) = x \\ log_{ {2}^{2} }( {2}^{ - 1} \times {2}^{ \frac{1}{3} } ) = x \\ { ({2}^{2} )}^{x} = {2}^{ - 1} \times {2}^{ \frac{1}{3} } \\ {2}^{2x} = {2}^{( - 1 + \frac{1}{3}) } \\ {2}^{2x } = {2}^{ - \frac{2}{3} } \\ 2x = - \frac{2}{3} \\ 6x = - 2 \\ x = - \frac{2}{6} \\ x = - \frac{1}{3}$

b)

$log_{0.2}0.04 = x \\ log_{ \frac{2}{10} }( \frac{4}{100} ) = x \\ ({ \frac{2}{10} })^{x} = \frac{4}{100} \\ { (\frac{2}{10} )}^{x} = ({ \frac{2}{10} )}^{2} \\ x = 2$

c)

$log_{0.04}0.2 = x \\ log_{ \frac{4}{100} }( \frac{2}{10} ) = x \\ ({ \frac{4}{100} )}^{x} = \frac{2}{10} \\ ({ \frac{2}{10} })^{2x} = \frac{2}{10} \\ 2x = 1 \\ x = \frac{1}{2}$