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pratu043 Group Title

Can someone please explain how to solve a log equation with an example.

  • 2 years ago
  • 2 years ago

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  1. dpaInc Group Title
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    how 'bout u pick an example....

    • 2 years ago
  2. dpaInc Group Title
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    otherwise i'll choose the easiest...:)

    • 2 years ago
  3. pratu043 Group Title
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    OK ... \[5^{x - 3} . 3^{2x-8} = 225\]

    • 2 years ago
  4. pratu043 Group Title
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    How to solve this using log? I'm new so I have no idea.

    • 2 years ago
  5. pratu043 Group Title
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    I mean new to log.

    • 2 years ago
  6. pratu043 Group Title
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    pls help.

    • 2 years ago
  7. lgbasallote Group Title
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    welcome to logarithms!

    • 2 years ago
  8. pratu043 Group Title
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    Yeah thanks!

    • 2 years ago
  9. waterineyes Group Title
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    I guess you can solve this without using Logs..

    • 2 years ago
  10. pratu043 Group Title
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    But I want to know how to do it with log.

    • 2 years ago
  11. waterineyes Group Title
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    Okay then all here will explain you how to do this...

    • 2 years ago
  12. moha_10 Group Title
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    15^(x-3)+(2x-8)=225 now we take ln (3x-11)15= ln225

    • 2 years ago
  13. pratu043 Group Title
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    What is In? And how did you get 15^(x-3)+(2x-8)=225?

    • 2 years ago
  14. moha_10 Group Title
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    15*ln(3x-11)=ln 225

    • 2 years ago
  15. moha_10 Group Title
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    by multi 3 into 5 to get 15 and the exponent it's added

    • 2 years ago
  16. pratu043 Group Title
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    But how can you just multiply the base and add the exponents?

    • 2 years ago
  17. waterineyes Group Title
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    Use the following formulas of Logs: \[\large Log(a \times b) = Log(a) + Log(b)\] \[\large Log(a)^b = b.Log(a)\]

    • 2 years ago
  18. moha_10 Group Title
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    before we take the logarithem

    • 2 years ago
  19. moha_10 Group Title
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    it's from exponent experepties

    • 2 years ago
  20. pratu043 Group Title
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    Why did you delete that @dpaInc?

    • 2 years ago
  21. dpaInc Group Title
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    because i don't wanna take away from these guys awesome explanations....:)

    • 2 years ago
  22. waterineyes Group Title
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    See, take Log both the sides you will get: \[\large Log(5^{x-3}.3^{2x-8}) = Log(225)\] Now use the formulas I have written above..

    • 2 years ago
  23. waterineyes Group Title
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    Use the first formula only...

    • 2 years ago
  24. pratu043 Group Title
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    \[\log(5^{x-3}) . \log(3^{2x-8}) = \log 225 \]

    • 2 years ago
  25. waterineyes Group Title
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    Now Check my first formula carefully...

    • 2 years ago
  26. moha_10 Group Title
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    @pratu043 trust take my answer

    • 2 years ago
  27. moha_10 Group Title
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    like what waterineyes did now

    • 2 years ago
  28. pratu043 Group Title
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    That's what I've done here right @waterineyes?

    • 2 years ago
  29. waterineyes Group Title
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    I give you an example: \[\large Log(2 \times 3) = Log(2) + Log(3)\] Go by this procedure...

    • 2 years ago
  30. pratu043 Group Title
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    I've already done that. So now we should use the second one?

    • 2 years ago
  31. waterineyes Group Title
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    You have done it wrongly my friend...

    • 2 years ago
  32. waterineyes Group Title
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    See check the formula.. After formula the result will be in sum form and your result is not in sum form.. Is there any + sign in your result???

    • 2 years ago
  33. pratu043 Group Title
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    Oops. \[\log(5^{x-3}) + \log(3^{2x-8}) = \log225\]

    • 2 years ago
  34. waterineyes Group Title
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    Yes now you are right... Now 225 is square of what number???

    • 2 years ago
  35. pratu043 Group Title
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    15

    • 2 years ago
  36. waterineyes Group Title
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    So can you write 225 as \(15^2\) on right hand side.?? If yes then do it..

    • 2 years ago
  37. pratu043 Group Title
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    \[\log(5^{x-3}) + \log(3^{2x-8}) = \log15^{2}\]

    • 2 years ago
  38. waterineyes Group Title
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    Now use the power rule of Logarithms that is the Second Formula that I have given above.. Can you use that??

    • 2 years ago
  39. waterineyes Group Title
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    I give you an example of that too: \[\large Log(x)^4 = 4.Log(x)\]

    • 2 years ago
  40. pratu043 Group Title
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    \[(x-3)\log5 + (2x-8)\log3 = 2\log15\]

    • 2 years ago
  41. waterineyes Group Title
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    Can you write 15 as 3*5??

    • 2 years ago
  42. pratu043 Group Title
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    Yes. \[(x-3)\log5 + (2x-8)\log3 = 2\log(5 * 3)\]

    • 2 years ago
  43. waterineyes Group Title
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    Then use it and use the first formula again on right hand side...

    • 2 years ago
  44. pratu043 Group Title
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    \[(x-3)\log5 + (2x-8)\log3 = 2\log5 + 2\log3\]

    • 2 years ago
  45. waterineyes Group Title
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    Now what you have to do is to compare the coefficients of \(Log3\) and \(Log5\) both the sides can you do that??

    • 2 years ago
  46. waterineyes Group Title
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    Tell me the coefficient of Log3 on Left hand side and right hand side...

    • 2 years ago
  47. pratu043 Group Title
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    On LHS its 2x - 8 and on RHS its 2.

    • 2 years ago
  48. waterineyes Group Title
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    Just equate them and find x from it..

    • 2 years ago
  49. waterineyes Group Title
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    Similarly equate the coefficients of log5 and then also find x you will get the same x in both the case...

    • 2 years ago
  50. waterineyes Group Title
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    No no...

    • 2 years ago
  51. pratu043 Group Title
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    \[(2x-8)\log3 = 2\log3\]

    • 2 years ago
  52. waterineyes Group Title
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    I said to equate the coefficients buddy.. Coefficients are 2x - 8 and 2.. you should equate this only...

    • 2 years ago
  53. pratu043 Group Title
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    So you should just do 2x-8 = 2?

    • 2 years ago
  54. pratu043 Group Title
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    x = 5

    • 2 years ago
  55. waterineyes Group Title
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    See, if : \[\large xlog3 = ylog3\] implies x = y. Getting??

    • 2 years ago
  56. pratu043 Group Title
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    Yes!!

    • 2 years ago
  57. waterineyes Group Title
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    Yes you have found x = 5 that is absolutely right...

    • 2 years ago
  58. pratu043 Group Title
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    Thanks a lot!!

    • 2 years ago
  59. waterineyes Group Title
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    Now equate the coefficients of log5..

    • 2 years ago
  60. pratu043 Group Title
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    x - 3 = 2 x = 2 + 3 = 5

    • 2 years ago
  61. waterineyes Group Title
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    Yes got the same value of x so you are right.. If anyhow x values are coming different then either question is wrong or your solution is wrong.. Getting??

    • 2 years ago
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