Question

calcule o valor da expressão (3log3⁴)log4⁸
me ajudem pfvor ​

Answer 1

Oie, tudo bom?

$= (3log_{3}(4) ) \: . \: log_{4}(8)$

$= 3 log_{3}(4) log_{2 {}^{2} }(2 {}^{3} )$

$= 3 log_{3}(4) \: . \: \frac{3}{2} \: . \: log_{2}(2)$

$= 3 log_{3}(4) \: . \: \frac{3}{2} \: . \: 1$

$= 3 log_{3}(4) \: . \: \frac{3}{2}$

$= \frac{3}{1} \: . \: log_{3}(4) \: . \: \frac{3}{2}$

$= \frac{3 \: . \: 3}{ 1\: . \: 2} \: . \: log_{3}(4)$

$= \frac{9}{2} \: . \: log_{3}(4)$

$= \frac{9}{2} \: . \: log_{3}(2 {}^{2} )$

$= \frac{9}{2} \: . \: 2 log_{3}(2)$

$\boxed{ = 9 log_{3}(2) }$

Att. NLE Top Shotta