## GOODMAN 3 years ago Write in exponential form. (Will write in equation editor)

1. GOODMAN

$5^{\log5}^{25}$

2. GOODMAN

wait..that came out funny..

3. GOODMAN

$5^{\log5}$

4. GOODMAN

There is suppoesd to be a 25 next to log 5

5. UnkleRhaukus

$5^{log{5}^{25}}$ ?

6. TuringTest

$\huge 5^{(\log5)^{25}}$?

7. UnkleRhaukus

is 5 the base of the logarithm ?

8. GOODMAN

Turing Test wrote it correctly.

9. GOODMAN

I know how to do it, just am confused about the 5 in the front. what do i do with it?

10. UnkleRhaukus

the the exponent of the log can come out the front $5^{log(5)^{25}}=5^{25(log(5)}$

11. GOODMAN

Thats it? I am still confused.

12. TuringTest

$5^{25\log5}\neq5^{25}\times5^{\log5}$

13. UnkleRhaukus

I have made an error turing test?

14. TuringTest

$\log_5(25)=2$you are tired

15. GOODMAN

I am reading this off of my math book. 5 is the big dog, while $\log _{5}25$ is above it.

16. UnkleRhaukus

oh yeah i see how wrong that is now

17. TuringTest

well now that we've got it sorted out the problem is trivial goodman please try to post more clearly, that is not what you originally wrote

18. UnkleRhaukus

errors ervery where, perhaps i should just watch and learn

19. GOODMAN

How did you get that? @TuringTest

20. TuringTest

$\huge 5^{\log_5(25)}=5^2=25$because$\huge 5^2=25$

21. GOODMAN

I appologize, srry, i did read it wrong. srry srry.

22. GOODMAN

I am new to log, so yea, srry.

23. TuringTest

but in general$\huge a^{\log_a(x)}=x$so we could have skipped that analaysis

24. GOODMAN

Oh yea, because it always is equal to the front number. Yea, okay, got it :D Thanx, srry for the mix up :/

25. TuringTest

it's ok, let me know if you have more questions

26. GOODMAN

You are familiar with log? Because dont understand em at all :P

27. TuringTest

yes, they can be a bit tricky at first think about small numbers first the definition as I like to give it:$\huge\log_ax=b\text{ if }a^b=x$in other words$\large \log_ax$asks "what power do we raise a to in order to get x?" for example...

28. TuringTest

$\large\log_2(4)$asks "2 raised to what power equals 4?" so what is the answer?

29. GOODMAN

2 rite?

30. TuringTest

right because 2^2=4 so what about$\log_2(16)$?

31. GOODMAN

4

32. TuringTest

right so now you should see why$\log_5(25)=2$yes?

33. GOODMAN

YES!! wow!! It is 5 because 5^5 is equal to 25

34. TuringTest

$5^2$

35. GOODMAN

Whoops..srry, so the exponent is the answer?

36. TuringTest

yeah$\log_2(16)=4$as you said, because$2^4=16$

37. GOODMAN

Is that always the case?

38. TuringTest

so$\log_5(25)=2$because$5^2=25$

39. TuringTest

in general we have$\huge\log_a(x)=y\iff a^y=x$so yes, that means always you could say that the question is on the left: "a to what power equals x?" the answer is on the right "a to the y equals x"

40. TuringTest

so do some more what is$\log_4(16)$?

41. GOODMAN

2

42. TuringTest

right$\log_{10}(10000)$ ?

43. GOODMAN

umm..lol, 1000

44. GOODMAN

I think i got it wrong

45. TuringTest

the question is "10 to what power equals 10000" you are asserting that$\large10^{1000}=10000$which I dont think you believe what is$10^2$ ?

46. GOODMAN

Wait..no, its 100

47. TuringTest

$10^{100}\neq10000$

48. GOODMAN

So what is it?

49. GOODMAN

I dont have a calculator rite now :P

50. TuringTest

$10^2=10\cdot10=100$$10^3=10\cdot10\cdot10=1000$the exponent on the ten is the number of zeros after the one so 10 to what power equals 10000 ?

51. GOODMAN

$10^{4}?$

52. TuringTest

exactly so$\log_{10}(10000)=4$because$10^4=10000$

53. GOODMAN

That makes its it so simple

54. TuringTest

yeah that's a handy rule, and is used in science to describe very large and small numbers last one: how about$\log_3(81)$

55. GOODMAN

4

56. TuringTest

right :D do you know the basic log rules$\log(ab)=\log a+\log b$$\log(\frac ab)=\log a-\log b$$\log(a^b)=b\log a$?

57. GOODMAN

No, we havent been taught those. We started log in class today.

58. TuringTest

when you start using that things will be easier $\large \log(ab)=\log a+\log b\text{ because }x^a\cdot x^b=x^{a+b}$for example it takes a bit to get used to those ideas though

59. GOODMAN

Yea, just by reading it, I understand the first function.

60. GOODMAN

I also understand the second one, the third one looks funny.

61. TuringTest

the third one can be illustrated by the problems we just did first I will ask you what is$\log_22$?

62. GOODMAN

1

63. GOODMAN

lol, i find myself saying "2 raised to what power is 2" thats a neat trick

64. TuringTest

I'm glad, it helps me! and in general$\log_aa=1$now look at$\log_2(16)$if we factor 16 we get$\log_2(2^4)$now apply the third rule$4\log_2(2)=4(1)=4$so we get the answer we already knew it also shows that$\log_aa^x=x$which is nice to know that's how I did your earlier problem) so by factoring and using these rules we can break down lots of numbers with logs

65. TuringTest

now here's the last grand example$\log_2(24)=\log_2(2^3\cdot3)$using the first rule$\log_2(2^3)+\log_23$and now the third$3\log_2(2)+\log_23=3+\log_23$and that's as far as it goes

66. GOODMAN

Wow, i never knew log could be so simple :D

67. TuringTest

I'm glad you feel that way :D

68. GOODMAN

Thanx a ton :D I am now cleared up on log, thank you thank you!!!

69. TuringTest

happy to help!