Question

Calcule os logaritmos como indicado.​

Answer 1

6)

a)

$\mathtt{ log_{8}( log_{3}(81)) = log_{8}(4)} \\ = \mathtt{ log_{ {2}^{3} }( {2}^{2} ) = \dfrac{2}{3} }$

b)

$log_{9}( log_{4}(32) ) + log_{4}( log_{3}(81) ) \\ = log_{9}( \frac{5}{2} ) + log_{4}(4) = log_{9}( \frac{5}{2}) + 1$

7)

$log_{5 \sqrt[3]{5} }(125) = log_{5. {5}^{ \frac{1}{3} } }(125) \\ = log_{ {5}^{ \frac{4}{3} } }( {5}^{3} ) = \dfrac{3}{ \dfrac{4}{3} } \\ = 3. \dfrac{3}{4} = \mathtt{\dfrac{9}{4} }$