Exercices - Logarithmes et exponentielles

Résoudre

1) ln^2[x] - ln(x) - 20

2) ln^4[x] - 3 ln^2[x] + 20

3) ln(x - 4) + ln(2 x - 3) 2 ln(5)

4) ln(2 x - 3) - ln(x - 4) 2 ln(5)

5) 2 ln(x - 3) + ln(x - 1)  ln(2 x - 2)

6) 20 ln^2[x] - 16 ln(x) + 30

7) 4^x - 2^(x + 3) - 1280

8) 3^(3 - x) + 3^x12

9) log_x(2^(1/2)) 3

10) log_6(x) + log_x(6) 13/6

11) 2 log_4(x + 1) + log_4(x + 3) log_4(6 x + 2) + 1/2

12) log_2(x - 1) log_4(3)

13) log_7(3 x - 1)  -1/2

14) log_3(log_4(x))  -1

15) log_2(log_x(81)) 2

16) -4 ^(-x) + ^x - 30

17) log_ (x - 1)(5 x) 2

18) -10^x + 10^(2 x) 5

19) 81^(1 - x) + 81^x30

20) log_10(x + 1) - 2log_5(0.2)

21) log_1/3((1 - x^2)/x) <log_3(x)

22) 4 - ln^2[x] ≤0

23) ln(x) - ln(2) ≤ ln(1 - 3 x)

24) (ln(x) + 1)/(1 - ln(x)) ≤0

25) 2 ln^2[x] - ln(x) - 1≥0

26) -3 + 2 ^(-x) + ^x>0

27) 1/ + ^(2 x + 1) >0

28) (1/)^x - ^(3 x - 1) ≤0

29) ln(x) + ln((x - 1)/(x + 1)) <0

30) ln(2 + ^x) ≥ ln(4 - ^x)

31) log_1/5(3 x - 1) ≤5

32) log_7((1 - x)/(x + 1)) ≥0

33) log_1/5(5) x

34) log_ (x - 4)(4 x) 2

35) 5^x^(1/2) + 2/5^x^(1/2) 3

Solutions

Created by Mathematica  (October 17, 2007)
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