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Math Help - ln or log problems im confused

  1. #1
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    ln or log problems im confused

    Hey guys I am new to this website and wanted some help. I would like to see the steps if possible. Thank you!

    Solve for t or x. Round off 3 significant decimals
    ln(t/t-2)=1
    5^(t+1)=6^t
    ln9x=1
    2=e^(.6t)
    1/5=e^(4x)
    9ln x = 15
    ln 3 + ln x= 1.4
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  2. #2
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    Quote Originally Posted by Jackie10 View Post
    Hey guys I am new to this website and wanted some help. I would like to see the steps if possible. Thank you!

    Solve for t or x. Round off 3 significant decimals
    ln(t/t-2)=1
    5^(t+1)=6^t
    ln9x=1
    2=e^(.6t)
    1/5=e^(4x)
    9ln x = 15
    ln 3 + ln x= 1.4
    I'll take you through them one at a time if you like, but first show me how you would start Q1.
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  3. #3
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    Quote Originally Posted by Jackie10 View Post
    Hey guys I am new to this website and wanted some help. I would like to see the steps if possible. Thank you!

    Solve for t or x. Round off 3 significant decimals
    ln(t/t-2)=1
    5^(t+1)=6^t
    ln9x=1
    2=e^(.6t)
    1/5=e^(4x)
    9ln x = 15
    ln 3 + ln x= 1.4
    \ln{\frac{t}{t - 2}} = 1

    \frac{t}{t - 2} = e^1

    \frac{t - 2 + 2}{t - 2} = e

    1 + \frac{2}{t - 2} = e

    \frac{2}{t - 2} = e - 1

    \frac{t - 2}{2} = \frac{1}{e - 1}

    t - 2 = \frac{2}{e - 1}

    t = \frac{2}{e - 1} + 2

    t = \frac{2}{e - 1} + \frac{2(e - 1)}{e - 1}

    t = \frac{2 + 2e - 2}{e - 1}

    t = \frac{2e}{e - 1}.
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  4. #4
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    Quote Originally Posted by Jackie10 View Post
    Hey guys I am new to this website and wanted some help. I would like to see the steps if possible. <<<<< we also
    Thank you!

    Solve for t or x. Round off 3 significant decimals
    ...
    5^(t+1)=6^t
    ...
    1. I assume that you are familiar with the basic laws of powers and logarithms.

    2.
    5^{t+1}=6^t

    5 \cdot 5^t=6^t

    5=\frac{6^t}{5^t}=\left(\frac65 \right)^t

    t=\log_{\frac65}(5)=\frac{\ln(5)}{\ln(6)-\ln(5)}
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  5. #5
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    Quote Originally Posted by Jackie10 View Post
    Hey guys I am new to this website and wanted some help. I would like to see the steps if possible. Thank you!

    Solve for t or x. Round off 3 significant decimals
    ln(t/t-2)=1
    5^(t+1)=6^t
    ln9x=1
    2=e^(.6t)
    1/5=e^(4x)
    9ln x = 15
    ln 3 + ln x= 1.4
    \ln(9x) = 1

    9x = e^1 = e\

    x = \frac{e}{9}
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  6. #6
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    Thank you!

    So for 2=e^.6t

    do i take
    ln of both sides

    ln2=lne^.6t

    then
    lne=1

    ln2=.6931

    .6931=.6t
    to get t i divide by .6 to both sides

    then i get

    .6931/.6

    t=1.155
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  7. #7
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Jackie10 View Post
    So for 2=e^.6t

    do i take
    ln of both sides

    ln2=lne^.6t

    then
    lne=1

    ln2=.6931

    .6931=.6t
    to get t i divide by .6 to both sides

    then i get

    .6931/.6

    t=1.155
    Correct!!
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