1. Вычислить: 1) log₁ 16; 2) 51+log53; 3) log3 135 log3 20 + 2 log3 6.

1. Вычислить:

1) $$log_{\frac{1}{2}} 16$$

$$log_{\frac{1}{2}} 16 = x$$

$$(\frac{1}{2})^x = 16$$

$$2^{-x} = 2^4$$

$$-x = 4$$

$$x = -4$$

2) $$5^{1+log_5 3}$$

$$5^{1+log_5 3} = 5^1 \cdot 5^{log_5 3} = 5 \cdot 3 = 15$$

3) $$log_3 135 - log_3 20 + 2 log_3 6$$

$$log_3 135 - log_3 20 + log_3 6^2 = log_3 \frac{135 \cdot 36}{20} = log_3 \frac{135 \cdot 9}{5} = log_3 (27 \cdot 9) = log_3 3^3 \cdot 3^2 = log_3 3^5 = 5$$

Ответ: 1) -4; 2) 15; 3) 5