Реши логарифмические уравнения.

Конечно, решим! Вот решения уравнений: 1. $\log_9 3^{5x-5} = 4$ $3^{5x-5} = 9^4$ $3^{5x-5} = 3^8$ $5x-5 = 8$ $5x = 13$ $x = \frac{13}{5} = 2.6$ 2. $\log_{81} 3^{2x-6} = 2$ $3^{2x-6} = 81^2$ $3^{2x-6} = 3^8$ $2x-6 = 8$ $2x = 14$ $x = 7$ 3. $\log_{16} 2^{2x-7} = 3$ $2^{2x-7} = 16^3$ $2^{2x-7} = 2^{12}$ $2x-7 = 12$ $2x = 19$ $x = \frac{19}{2} = 9.5$ 4. $\log_{27} 3^{5x+5} = 2$ $3^{5x+5} = 27^2$ $3^{5x+5} = 3^6$ $5x+5 = 6$ $5x = 1$ $x = \frac{1}{5} = 0.2$ 5. $\log_4 2^{8x+8} = 4$ $2^{8x+8} = 4^4$ $2^{8x+8} = 2^8$ $8x+8 = 8$ $8x = 0$ $x = 0$ 6. $\log_8 2^{3x+9} = 4$ $2^{3x+9} = 8^4$ $2^{3x+9} = 2^{12}$ $3x+9 = 12$ $3x = 3$ $x = 1$ 7. $\log_2 (-5x - 6) = 6$ $-5x - 6 = 2^6$ $-5x - 6 = 64$ $-5x = 70$ $x = -14$ 8. $\log_3 (-10x - 14) = 4$ $-10x - 14 = 3^4$ $-10x - 14 = 81$ $-10x = 95$ $x = -9.5$ 9. $\log_2 (-7 - 3x) = 5$ $-7 - 3x = 2^5$ $-7 - 3x = 32$ $-3x = 39$ $x = -13$ 10. $\log_5 (-10 - 3x) = 3$ $-10 - 3x = 5^3$ $-10 - 3x = 125$ $-3x = 135$ $x = -45$ **Ответы:** 1. $x = 2.6$ 2. $x = 7$ 3. $x = 9.5$ 4. $x = 0.2$ 5. $x = 0$ 6. $x = 1$ 7. $x = -14$ 8. $x = -9.5$ 9. $x = -13$ 10. $x = -45