Question

Socorro me ajudem (Logaritmos)

Answer 1

$a) ~log5 ^{ \sqrt[5]{5} } = x$
$5^x= \sqrt[5]{5}$
$\not5^x = \not5^ \frac{1}{5} }$
$x= \frac{1}{5}$

$b) ~log4 ^{ \sqrt[3]{ \frac{2}{2} } } = x$
$4^x =( \frac{2}{2}) ^ \frac{1}{3}$
$\not2 ^{2x} = \not2 ^{ \frac{1}{3} -1}$
$2x= \frac{1}{3} - 1~~~~~~~~~~mmc = 3$
$6x =1-3$
$6x = -2$
$x= \frac{-2 ^{:2} }{6 ^{:2} }$
$x = - \frac{1}{3}$

$c) ~log~0,2~ ^{0,04} = x$
$( \frac{2}{10} )^x = \frac{4}{100}$
$\not( \frac{2}{10} )^x = \not\n (\frac{2}{10} ) ^2$
$x= 2$

$d)~ log8 ^{ \sqrt[3]{16} } =x$
$2^{3x} =( 2^4)^ \frac{1}{3}$
$\not2 ^{3x} = \not2^ \frac{4}{3}$
$3x = \frac{4}{3}$
$x= \frac{4}{9}$