Показательные уравнения

1. \(2^{x-1}\cdot 3^x=0,5\cdot 6^{2-x}\)
2. \((1-\frac{2x}{3})^{3x^2+17x+20}=1\)
3. \(|x-5|^{3x^2-15x}=1\)
4. \(3^{x\log_35}\cdot 5^{x^2-3x}=1\)
5. \(3^{|x|}=5^{x^2+3x}\)
6. \(3^{2^x}=2^{3^x}\)
7. \(3^x\cdot 8^{\displaystyle\frac{x}{x+2}}=6\)
8. \(3^{\displaystyle\frac{x+2}{3x-4}}-7=2\cdot 3^{\displaystyle\frac{5x-10}{3x-4}}\)
9. \((26+15\sqrt{3})^x-5(7+4\sqrt{3})^x+6(2+\sqrt{3})^x+(2-\sqrt{3})^x=5\)
10. \(2^{2x+1}-15\cdot 2^x+10=6\cdot |2^{x-1}-1|\)
11. \(3^{x+1}+3^{x-1}+3^{x-2}=5^x+5^{x-1}+5^{x-2}\)
12. \(5^{x+\frac{1}{2}}-9^x=3^{2x-2}-5^{x-\frac{1}{2}}\)
13. \(12^x+6^x-2\cdot 4^x-2\cdot 3^x-2^{x+1}+4=0\)
14. \(2^x+2^{\frac{1}{x}}=4\)

Ответы

1. 1
2. -4; -3; -5/3
3. 0; 4; 6
4. 0; 2
5. 0; \(-3-\log_53\)
6. \(\log_{2/3}\log_32\)
7. 1; \(-2-2\log_32\)
8. 2
9. -1; 1
10. 3; \(\log_2(3-\sqrt{7})\)
11. 2
12. 3/2
13. 0; \(\log_32\)
14. 1