## Egirl01 Group Title 2log(x-3)+1 = 5 Could you break it down step by step? I'm a bit confused on how to do this algebraically one year ago one year ago

1. Callisto Group Title

To solve x?

2. Egirl01 Group Title

yes, i presume

3. Callisto Group Title

Okay, first, subtract both sides by 1, what do you get?

4. Egirl01 Group Title

you get 2log(x-3) = 4

5. Callisto Group Title

Right, now divide both sides by 2, what do you get?

6. Egirl01 Group Title

log(x-3) = 2

7. Egirl01 Group Title

haha, that's fine :)

8. calculusfunctions Group Title

Don't mind me. @Callisto seems to be doing a fine job teaching so I'll just observe if you don't mind? I'll only respond if you ask.

9. Callisto Group Title

Yup! Now, take anti-log for both sides. What do you get? Note: anti-log = inverse of log For example, logx = 1 => 10^(logx) = 10^1 => x = 10^1 = 10

10. Egirl01 Group Title

yikes, haha, i'm not for sure. I briefly remember anti-logs but I'm not for sure what do with them

11. Callisto Group Title

Do you understand that example?

12. Egirl01 Group Title

i'm starting to get it. logx = 1. I understand that but not after that

13. calculusfunctions Group Title

If I may, @Callisto perhaps he'd @Egirl01 would understand if you asked her to change the logarithm form to exponential form. @Egirl01 do you know how to do that.

14. Egirl01 Group Title

No, I'm sorry

15. Egirl01 Group Title

give me one second

16. ByteMe Group Title

$$\large b^x=y \rightarrow log_by=x$$

17. Egirl01 Group Title

log^2 = x-3?

18. Callisto Group Title

logx = 1 is actually just an example... ---------------------------------- Intuitively, log a number is the value of the power of the base Let say, I have a number 100, which can be rewritten as 10^2 Now, I take log (base 10) of that number (100), so I'll get 2, since 10 to the power of 2 give me 100. (Sorry if I make it even worse...)

19. Egirl01 Group Title

No, I understand the piece. so if its simply log, then its naturally log10, and the anti-log of log10 is 1/10 right?

20. Callisto Group Title

anti-log of log 10 is 10. $\log^{-1}(log10) = 10$ anti-log is the inverse of log.

21. Egirl01 Group Title

Alright. So then it'd be 10 (x-3) = 2?

22. Callisto Group Title

No.... How did you get that?

23. Egirl01 Group Title

the anti-log of log 10 is 10, so log(x-3) = 2 would turn to 10(x-3) = 2? Obviously that is wrong. I'm a bit lost but you can continue onto the next part of solving the equation. I'll eventually figure what I'm doing wrong

24. Callisto Group Title

$log(x-3) = 2$Take anti-log for both sides: $\log^{-1}(log(x-3)) = \log^{-1}(2)$ Perhaps you can simplify the left first.

25. Egirl01 Group Title

I still don't quite follow, but continue on. I'll understand eventually :)

26. Callisto Group Title

Nope.. It's your turn to work on it... Which part you don't understand ?

27. Egirl01 Group Title

how exactly I create the anti-log from log(x-3)

28. Callisto Group Title

Because you are doing something on both sides... You create anti-log to undo the work of log...

29. Egirl01 Group Title

So the anti-log of log10 is 10, right? and the anti-log of 2 is what?

30. Callisto Group Title

31. Egirl01 Group Title

okay

32. Callisto Group Title

What is log10?

33. Egirl01 Group Title

log10 =1

34. Callisto Group Title

What is log100?

35. Egirl01 Group Title

log100 = 2

36. Callisto Group Title

Can we tell me what number do I have to take log on in order to get 1?

37. Egirl01 Group Title

10?

38. Callisto Group Title

Yes. So, what number do I have to take log on in order to get 2?

39. Egirl01 Group Title

100

40. Callisto Group Title

Yes! How did you get this answer?

41. Egirl01 Group Title

because you inversed it?

42. Callisto Group Title

Yes! So, now, can you answer your question? what is $$\log^{-1}2$$?

43. Egirl01 Group Title

It is 100

44. Callisto Group Title

Yes!

45. Egirl01 Group Title

So 10(x-3) = 100?

46. Callisto Group Title

No. Another set question questions... What is log10 (again)?

47. Egirl01 Group Title

log 10 is 1

48. Callisto Group Title

You got it right for the right side, it's wrong for the left.

49. Callisto Group Title

What is $$\log^{-1}log(10)$$?

50. Egirl01 Group Title

10

51. Callisto Group Title

Yes. What is $$\log^{-1}(log100)$$?

52. Egirl01 Group Title

2?

53. Egirl01 Group Title

WAIT

54. Egirl01 Group Title

100?

55. Callisto Group Title

Yes!

56. Callisto Group Title

What is $$\log^{-1} (log1000)$$?

57. Egirl01 Group Title

1000

58. Callisto Group Title

So, we can see that $$\log^{-1}$$ of log a number is the number itself, agree?

59. Egirl01 Group Title

yes

60. Callisto Group Title

So, $$\log^{-1} (\log y) = y$$, agree?

61. Egirl01 Group Title

yes

62. Callisto Group Title

So, what is $$\log^{-1} (log(x-3))$$?

63. Egirl01 Group Title

x-3?

64. Callisto Group Title

Yes!

65. Callisto Group Title

Can you simplify the following now? $\log^{-1}(log(x-3)) = \log^{-1}(2)$

66. Egirl01 Group Title

x-3 = 100?

67. Callisto Group Title

Yes! Now can you solve it?

68. Egirl01 Group Title

yes

69. Egirl01 Group Title

x = 103?

70. Callisto Group Title

Nice :D and Yes! Do you understand how to solve this type of question now?

71. Egirl01 Group Title

yes! Thank you soooo much for your help! I really appreciate it!

72. Callisto Group Title

You're welcome :)