43. a) 5log₂9 ⋅ log₃64 + 3^(log₆8) ⋅ 2^(log₆8);

a) Решим пример по действиям: 1) $$log_2 9 = log_2 3^2 = 2log_2 3$$ $$5log_2 9 = 5 \cdot 2log_2 3 = 10log_2 3$$ 2) $$log_3 64 = log_3 2^6 = 6log_3 2$$ 3) $$10log_2 3 \cdot 6log_3 2 = 60 log_2 3 \cdot log_3 2 = 60 \cdot \frac{log_2 3}{1} \cdot \frac{1}{log_2 3} = 60$$ 4) $$3^{log_6 8} \cdot 2^{log_6 8} = (3 \cdot 2)^{log_6 8} = 6^{log_6 8} = 8$$ 5) $$60 + 8 = 68$$ Ответ: 68