## anonymous 5 years ago Does anyone knows a really good book where I can learn about logarithms? I want a lot of theory and a million exercises.

1. anonymous

logarithms arent fun

2. anonymous

I think the theory behind logarithms would lie in number theory

3. anonymous

also there is literally only like 4 things you need to any logarithm question

4. anonymous

you dont need "a million exercises"

5. anonymous

"logarithms arent fun" is that a book or is that what you think?

6. anonymous

yeh its a book :p

7. anonymous

Im trying to solve a lot of equations, inequalities, doing graphs, etc

8. anonymous

im out trying to promote my online tutoring....i tutor math and physics from low - hgh level....if u ever need it check me out http://mathphystut.tripod.com

9. anonymous

I know the theory behind logarithm in general, but i want something really challenging

10. anonymous

Solve $2\ln(\sqrt{x}) - \ln(x) =1$

11. anonymous

an example

12. anonymous

but its all relatively standard

13. anonymous

You want challenging problems, or you want to clear your concept?

14. anonymous

want challenging problems

15. anonymous

yeh, well logarithms are that challenging to be honest

16. anonymous

arent*

17. anonymous

You can try one thing. You email me, and I will send you challenging problems

18. anonymous

As many as you want

19. anonymous

sure. can you give me your e-mail?

20. anonymous

About the problem above, elecengineer, I got 0=1. Is that right?

21. anonymous

Thanks "pi" I just sent you an email. Can you check it out

22. anonymous

It must take a little bit. Im from Ecuador and I suppose your in Europe lol

23. anonymous

24. anonymous

Can you check it out again. Can take a little bit

25. anonymous

differentiate $y= \ln [\frac{ (x-3)^4 \sqrt{x} }{x+1} ]$

26. anonymous

thats prob the hardest question on logarithms every, but its still really easy

27. anonymous

Okay code is VILLAMAGUA CONZA LUIS MIGUEL VILLAMAGUA CONZA LUIS MIGUEL

28. anonymous

yean. I got 4LN(x-3)+1/2(LN(x))-LN(X+) cannot remember how to differenciate logs lol

29. anonymous

just joking

30. anonymous

yeah it is me PI, thanks for your help

31. anonymous

I have sent you a problem, but remember, you are not supposed to use a calculator

32. anonymous

lols, what was it

33. anonymous

By the way, are you a staff of UTPL ?

34. anonymous

what was the question!

35. anonymous

yeah. From UTPL

36. anonymous

You teach there?

37. anonymous

No teaching, but a student. Well finishing my major

38. anonymous

solve simultaneously $5^{x+y} = \frac{1}{5}\ and \[5^{3x+2y} =1$

39. anonymous

$5^{x+y} = \frac{1}{5} , 5^{3x+2y} =1$

40. anonymous

I just replied you first question PI. Is that all right?

41. anonymous

there fairly standard lol all of logarithms are fairly standard. I have no idea why people find them hard , all it is is 4formulas to remember

42. anonymous

I dont know much about inequalities with logs.

43. anonymous

yeh , they come up a tiny bit in some financial maths topics

44. anonymous

inequalities and logs dont come up alot there is however one thing which you do need to look out for when solving inequalities with logs

45. anonymous

best seen by an example

46. anonymous

When I was in high school logarithms seems to be so hard. Now I tried them again and they look so easy. Im confused. I thought I would never be done with logs

47. anonymous

solve (1/3)^n > 0.5

48. anonymous

solve that, and see what happens

49. anonymous

ok

50. anonymous

I will put money on you being wrong :P

51. anonymous

it looks fairly simple, but there is a trick in it that would catch alot of people

52. anonymous

please dont go. Im a little bit slow. I like this :)

53. anonymous

well ... have you done the question yet inequalities with logs behave the exact same as equations

54. amistre64

the bigger n is.... the .......

55. anonymous

This is what i got

56. anonymous

long way to go about things also you would need to use change of basic at the end if you actually wanted to get a number for it

57. anonymous

What is the other wat? Im excited lol

58. anonymous

what is the other way? sorry

59. anonymous

well the way I was taught was to take logarithms of both sides ( it doesnt matter what base, as long as you use the same on both sides ) so I will take ln of both sides so $\ln [( \frac{1}{3})^n] = \ln(0.5)$

60. anonymous

now $\log_{a} x^r = r \log_{a} x$

61. anonymous

yeah. I know where you go

62. anonymous

63. anonymous

so then you get n ln(1/3) >0.5

64. anonymous

*so then you get n ln(1/3) > ln(0.5)

65. anonymous

$n > \frac{\ln(0.5)}{\ln(\frac{1}{3} ) }$

66. anonymous

there the problem people make!

67. anonymous

mm, I divide both sides by ln(1/3) , but am I allowed to do that? well , ln(1/3) is actually a negative number , so I must flip the inequality sign

68. anonymous

ln(a) is negative for all a in the interval 0<a<1

69. anonymous

Yeah I would have fallen there too. Can you email me some of this type of exercices.