(log5 (2)- log 5(4))/log3 (16)-log 5 (0.5))

   1. Преобразуем заданное выражение, обозначив его Z:

      Z = {log5(2) - log5(4)} / {log3(16) - log5(0.5)};

      Z = log5(2 / 4) / {log3(2^4) - log5(1/2)};

      Z = log5(1/2) / {4log3(2) - (log5(1) - log5(2))};

      Z = {log5(1) - log5(2)} / {4log3(2) + log5(2)};

      Z = {-1 / log2(5)} / {4 / log2(3) + 1 / log2(5)};

      Z = {-1 / log2(5)} / {(4log2(5) + log2(3)) / (log2(3) * log2(5))};

      Z = -log2(3) / {4log2(5) + log2(3)};

      Z = -log2(3) / log2(3 * 625);

      Z = -log2(3) / log2(1875);

      Z = -1 / log3(1875).

   Ответ: -1 / log3(1875).