1) log4 80 / (2 + log4 5) 2) log 2 (корень из 15) 3375 3) log 16 * log2 16 4) log2/5 корень из 2,5 5) log9 25 (корень из 12) / log9 12

1) log₄ 80 / (2 + log₄ 5) = log₄ 80 / (2log₄ 4 + log₄ 5) = log₄ 80 / (log₄ 4² + log₄ 5) = log₄ 80 / log₄ (16 * 5) = log₄ 80 / log₄ 80 = 1;

2) log_{2 (sqrt15)} 3375 = log_{2 (sqrt15)} 15³ = 3 log_{2 (sqrt15)} 15 = 3 * log₁₅ 15/log₁₅ 2sqrt15 = 3 / (log₁₅ sqrt15 + log₁₅ 2) = 3 / (1/2 + log₁₅ 2);

3) log 16 * log₂ 16 = log₁₆ log₂ 2^4 = log₁₆ 4 = log_4^2 4 = 1/2;

4) log_2/5 sqrt2,5 = log_2/5 sqrt5/2 = log_2/5 5/2^1/2 = 1/2log_2/5 5/2 = 1/2 * (-1) = - 1/2;

5) log₉ 25 (sqrt12) / log₉ 12 = log₉ 12^1/25/log₉ 12 = 1/25.