Results 1 to 9 of 9

Math Help - Some logarithms to check (With Work Part 1 of 4)

  1. #1
    Member
    Joined
    Aug 2009
    Posts
    113

    Some logarithms to check (With Work Part 1 of 4)

    Please check the following logarithms and let me know if they are correct. If they are not, please point out the mistake I am making and what to fix You will be thanked

    1. 4^x = 64

    ln(4^x) = ln(24)
    xln(4) = ln(24)
    xln(4)/ln(4) = ln(24)/ln(4)
    x = ln(24)/ln(4)


    2. log4(64) = 3


    3. y = e^3

    e^3 = y
    e = 3SQRT(y)


    4. log(x) + log(x) = 2

    2(log(x)) + 2(-1) = 0
    2(log(x)-1) = 0
    (log(x)-1) = 0
    log(x)-1 = 0
    log(x) = 1
    10log(x) = 10
    x = 10


    5. 2log(x) - log(x^2) + log(2/x) + log(x)

    log(x^2) - log(x^2) + log(2/x) + log(x)
    log(x^2/x^2) + log(2/x) + log(x)
    log((x^2/x^2)(2/x))+log(x)
    log(((x^2/x^2)(2/x))(x))
    log(x((x^2/x^2)(2/x)))
    log(x((x^2/x^2) * 2/x))
    log(x((1)*2/x))
    log(x(2(1)/x))
    log(x(2*1/x))
    log(x(2/x))
    log((1 * 2))
    log((2))
    log(2)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member malaygoel's Avatar
    Joined
    May 2006
    From
    India
    Posts
    648
    Quote Originally Posted by bobbyboy1111 View Post
    Please check the following logarithms and let me know if they are correct. If they are not, please point out the mistake I am making and what to fix You will be thanked

    1. 4^x = 64

    ln(4^x) = ln(24)
    xln(4) = ln(24)
    xln(4)/ln(4) = ln(24)/ln(4)
    x = ln(24)/ln(4)

    You just changed 64 into 24
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2009
    Posts
    113
    Quote Originally Posted by malaygoel View Post
    You just changed 64 into 24
    Is this wrong? How do I fix it if so? What about the rest of the problems, are they correct?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member malaygoel's Avatar
    Joined
    May 2006
    From
    India
    Posts
    648
    Quote Originally Posted by bobbyboy1111 View Post
    [LEFT]Please check the following logarithms and let me know if they are correct. If they are not, please point out the mistake I am making and what to fix You will be thanked

    1. 4^x = 64

    ln(4^x) = ln(24)
    xln(4) = ln(24)
    xln(4)/ln(4) = ln(24)/ln(4)
    x = ln(24)/ln(4)

    1. 4^x = 64

    ln(4^x) = ln(64)
    xln(4) = ln(64)
    xln(4)/ln(4) = ln(64)/ln(4)
    x = ln(64)/ln(4)
    x=3

    Rest are correct.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Aug 2009
    Posts
    113
    I appreciate your help very much! There is more to come soon
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member malaygoel's Avatar
    Joined
    May 2006
    From
    India
    Posts
    648
    Quote Originally Posted by bobbyboy1111 View Post

    3. y = e^3

    e^3 = y
    e = 3SQRT(y)

    also
    y=log_e 3
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Aug 2009
    Posts
    113
    Quote Originally Posted by malaygoel View Post
    also
    y=log_e 3
    So...

    y = loge^3

    loge^3 = y
    e = 3SQRT(y) ???
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member malaygoel's Avatar
    Joined
    May 2006
    From
    India
    Posts
    648
    Quote Originally Posted by bobbyboy1111 View Post
    So...

    y = loge^3

    loge^3 = y
    e = 3SQRT(y) ???
    My mistake.

    Here is correct

    y=e^3

    if you solve for e, then
    e=\sqrt[3]{y}........you are correct

    otherwise, if take logarithms both sides
    logy=loge^3
    logy=3loge
    \frac{logy}{loge}=3
    log_e y=3
    ln(y)=3
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    Quote Originally Posted by bobbyboy1111 View Post
    Is this wrong?
    Yes, changing "64" to "24" changes the number, thus changing the equation and the solution.

    Quote Originally Posted by bobbyboy1111 View Post
    How do I fix it if so?
    Correct the typo: replace the "2" with the original "6".
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: March 12th 2011, 05:05 AM
  2. Replies: 0
    Last Post: August 17th 2010, 09:29 AM
  3. Replies: 2
    Last Post: August 16th 2010, 08:09 AM
  4. Replies: 3
    Last Post: August 9th 2009, 05:01 AM
  5. Logarithms Part 2
    Posted in the Algebra Forum
    Replies: 5
    Last Post: October 28th 2007, 11:32 AM

Search Tags


/mathhelpforum @mathhelpforum