Issolvi -{left(log_{2}({1/5})right)}^frac{3{5}}-{left(log_{2}({2/5})right)}^frac{2{5}}=-log_{2}({{left(1/5right)}^frac{3{5}}{left(2/5right)}^frac{2{5}}})

$$- { \left( \log_{ 2 }({ \frac{ 1 }{ 5 } }) \right) }^{ \frac{ 3 }{ 5 } } - { \left( \log_{ 2 }({ \frac{ 2 }{ 5 } }) \right) }^{ \frac{ 2 }{ 5 } } = - \log_{ 2 }({ { \left( \frac{ 1 }{ 5 } \right) }^{ \frac{ 3 }{ 5 } } { \left( \frac{ 2 }{ 5 } \right) }^{ \frac{ 2 }{ 5 } } })$$

Evalwa (complex solution)

$$e^{\frac{8\pi i}{5}}\left(\log_{2}\left(5\right)\right)^{\frac{3}{5}}-\left(\log_{2}\left(\frac{2}{5}\right)\right)^{\frac{2}{5}}=\log_{2}\left(5\right)-\frac{2}{5}$$

Ivverifika