Question

Cum se rezolva acest exercitiu: $log_{ \sqrt[3]{2} }( log_{ \sqrt{5} } 625)=?$

Answer 1

$\displaystyle log_{ \sqrt[3]{2} }(log_{ \sqrt{5} } 625)=log_{ \sqrt[3]{2} }\left( \frac{1}{ \frac{1}{2} } log_5625\right)=log_{ \sqrt[3]{2} }(2log_5625)= \\ \\ =log_{ \sqrt[3]{2} }(2log_55^4)=log_{ \sqrt[3]{2} } (4 \cdot 2 log_55)=log_{ \sqrt[3]{2} }(4 \cdot 2)= \\ \\ =log_{ \sqrt[3]{2} }8= \frac{1}{ \frac{1}{3} }log_28=3 log_28=3log_22^3=3 \cdot 3log_22=3 \cdot 3=9$