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## anonymous one year ago Check this.? Im not very good with logarithms and i watched a video and it said to do it like this but im not sure Log\/2(3)+log\/2(x)=3 then cancel out the logs as they are the same base so, 3+x=3 -3 -3 x=0???

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1. Nnesha

what's the original question ?

2. anonymous

Log\/2(3)+log\/2(x)=3

3. Nnesha

i mean equation $\log_2(3)+\log_2 x=3$ like this OR

4. Nnesha

$\frac{ \log_2 3 }{ \log_2 x} =3$

5. Nnesha

maybe or maybe division hmm which one is correct ? graysongraddyLOL

6. anonymous

the first one is the original

7. Nnesha

oh okay familiar with the log properties ??

8. anonymous

Not exactly.

9. Nnesha

quotient rule$\large\rm log_b x - \log_b y = \log_b \frac{ x }{ y}$ to condense you can change subtraction to division product rule $\large\rm log_b x + \log_b y = \log_b( x \times y )$ addition ----> multiplication power rule $\large\rm log_b x^y = y \log_b x$

10. Nnesha

look at that and tell me which one you should apply ?

11. anonymous

The last one.?

12. anonymous

Math just absolutely dumbfounds me.

13. Nnesha

hmm alright there is PLUS sign between log now look at the log identities

14. anonymous

the subexponent of 2 is the identity correct.?

15. Nnesha

2 is base

16. Nnesha

quotient rule$\large\rm\color{reD}{ log_b x - \log_b y = \log_b \frac{ x }{ y}}$ to condense you can change subtraction to division product rule $\large\rm \color{reD}{log_b x + \log_b y = \log_b( x \times y )}$ addition ----> multiplication power rule $\large\rm \color{Red}{log_b x^y = y \log_b x}$ you don't need ^power rule for this e quation we should apply it when there is a number at front of log

17. anonymous

so with the equation that i am using, How do i get a Log on the other side of the equal sign.?

18. Nnesha

alright we need to apply product rule which is $\large\rm \color{reD}{log_b x + \log_b y = \log_b( x \times y )}$ log_b same base so take it out and multiply x y $\log_b x+ \log_b y$ $\log_b (x \times y)$

19. anonymous

So multiply 3 and x.?

20. Nnesha

$\huge\rm log_2(3)+\log_2 x=3$ like this OR yes right!!

21. Nnesha

that's how we should condense log equations $\huge\rm log_2 (3 \times x)=3$ now we should convert log to exponential form

22. Nnesha

|dw:1439575720373:dw|

23. anonymous

That just absolutely confused me.

24. Nnesha

well you will see how easy it's just have to move that variables around

25. Nnesha

right side term becomes exponent of base and move the left side term to the right side |dw:1439575981638:dw|

26. anonymous

so log2 (3) = 3x.?

27. Nnesha

we need to convert to exponential there shouldn't be an log b=2 how would write 2 with 3 exponent ?

28. Nnesha

2 to the 3 ppower

29. anonymous

so 2^3=3?

30. Nnesha

2^3 = 3x not just x

31. Nnesha

now solve for x

32. anonymous

$x=\frac{ 8 }{ 3 }$

33. Nnesha

:)

34. anonymous

Okay cool :)

35. anonymous

Can you give me a example logarithm so i can see if i got the hang of it.?

36. Nnesha

why not!!

37. anonymous

Thank you so much :D

38. Nnesha

$\huge\rm log_3 (4) - \log_3 (y) = 2$ look at the log properties

39. anonymous

So id use the first one right.?

40. Nnesha

yea quotient property

41. anonymous

then it would go to $\log_{3}(4 \div x)=3$

42. Nnesha

yep right

43. Nnesha

it's y not x but it's okay :P

44. Nnesha

i'm not gonna take off points like teachers do lol

45. anonymous

Oh whoops lol

46. anonymous

So it would go to $3^{4}=3x$

47. Nnesha

hmm no

48. anonymous

Where did i go wrong.?

49. Nnesha

the number which is opposite of the log supposed to be the exponent of base $\log_3 ( \frac{ 4 }{ x }) =2$ and btw it's equal to 2 i would take off points for this mistake

50. Nnesha

try again!

51. anonymous

okay so it would go to $\frac{ 4 }{ x } = 2x$

52. Nnesha

how did you get two x's ?

53. anonymous

wait it would just be 2 on the right side

54. anonymous

then i multiply 4 from the left side to get 8 on the right side so x=8.?

55. Nnesha

|dw:1439577454761:dw|

56. Nnesha

here is the example to convert log to exponential form $\huge\rm log_\color{ReD}{b} x = \color{blue}{y}$ b is base $\huge\rm \color{ReD}{b}^\color{blue}{y} =x$

57. anonymous

$3^{2} =4x.?$

58. Nnesha

not really hmm it's 4/x so that would stay same at right side $3^2=\frac{ 4 }{ x }$now solve for x

59. anonymous

$x=\frac{ 4 }{ 9 }$

60. Nnesha

yep!

61. anonymous

Thank you so much!

62. Nnesha

my pleasure!

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