Εκθετικές - λογαριθμικές εξισώσεις [17]

Να λυθούν οι εξισώσεις:

1. \(15 = 12 + 5{{\bf{e}}^{10\,w - 7}}\)
2. \(4{{\bf{e}}^{2\,x + {x^{\,2}}}} - 7 = 2\)
3. \(8 + 3{{\bf{e}}^{4 - 9\,z}} = 1\)
4. \(4{t^2} - 3{t^2}{{\bf{e}}^{2 - t}} = 0\)
5. \(7x + 16x{{\bf{e}}^{{x^{\,3}} - 5x}} = 0\)
6. \(3{{\bf{e}}^{7\,t}} - 12{{\bf{e}}^{8\,t + 5}} = 0\)
7. \(2y{{\bf{e}}^{{y^{\,2}}}} - 7y{{\bf{e}}^{1 - 5\,y}} = 0\)
8. \(16 + 4\ln \left( {x + 2} \right) = 7\)
9. \(\displaystyle 3 - 11\ln \left( {\frac{z}{{3 - z}}} \right) = 1\)
10. \(2\log \left( w \right) - \log \left( {3w + 7} \right) = 1\)
11. \(\ln \left( {3x + 1} \right) - \ln \left( x \right) = - 2\)
12. \(t\log \left( {6t + 1} \right) - 3{t^2}\log \left( {6t + 1} \right) = 0\)
13. \(2\log \left( z \right) - \log \left( {{z^2} + 4z + 1} \right) = 0\)
14. \(\ln \left( x \right) + \ln \left( {x - 2} \right) = 3\)
15. \(11 - {5^{9w - 1}} = 3\)
16. \(12 + {20^{7 - 2t}} = 50\)
17. \(1 + {3^{{z^2} - 2}} = 5\)