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IES Santiago Sobrequés i Vidal

Departament de Matemàtiques

EQUACIONS EXPONENCIALS I LOGARÍTMIQUES

1. 2x+1 = 1024 R: x = 9

2. (1/3)2x-1 = 27 R: x = -1

3. [pic] R: x = -3/2

4. 5x-5 = 10 R: x = 6’430677

5. 6 = (1/4)x-3 R: x = 1’707519

6. 0’5 = 73x-5 R: x = 1’547931

7. 7x+2 – 2·7x = 72x+2 + 40/7 R: x = -1 i x = - 0’104290963

8. 5x/2 + 99 =4(5x + 1) R: x = 2 i x = 1’936259369

9. 4x + 2x-1 = 2x+2 + 2 R: x = 2

10. (32x – 3x) / (32x-1 + 32x-2) = 63/32 R: x = 1’892789261

11. 3·42x + 5·4x = 43x – 5(42x – 4x) – 43x/5 R: 0’660964047

12. 10x + 102x = 0’1-x · 102 + 100 R: x = 2

13. 3x + 3x-1 + 3x-2 = 13/81 R: x = -2

14. logx + log(x-1) = log6 R: x = 3

15. log5(2x + 1) = 1 R: x = 2

16. log3(5 – x) = 2 R: x = -4

17. log3(x + 1) + log3(x – 1) = log3(8/3) + log3x R: x = 3

18. 2log7x – log7(x + 1) = log7x + log7(28/5) – 1 R: x = 4

19. (1/2)log5x + 2 = log5(8x + 3) R: x = 9 i x = 1/64

20. log2(x + 2) + log2(x – 2) = log23 + log2x R: x = 4

21. log7(x + 3) – log7(x – 1) – log7(2x + 1) = 0 R: x = 2

22. (1/2)log4x = log4(x + 3) – 1 R: x = 9 i x = 1

23. log5x2 – 2(log5x - 3) – 3 = (3/2)log5(x – 15) R: x = 40

24. log3(x2 – 9) – log3(x – 3) = 1 + log3(x – 15) R: x = 24

25. [log2 + log(11 – x2)( / log(5 – x) = 2 R: x= 3 i x = 1/3

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