# LOGical equation

**Number Theory**Level 4

\(For\quad how\quad many\quad different\quad values\quad of\quad "w"\quad can\quad this\quad equation\quad be\quad satisfied?\\ \\ \log _{ x }{ \left( { p }^{ w }+{ q }^{ w } \right) } =w\\ \\ All\quad given\quad variables\quad are\quad natural\quad numbers.\)