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Math Help - solve equation for n where n is an exponent

  1. #1
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    solve equation for n where n is an exponent

    Please help me with the following sum:

    Dermine n if:
    665/24=(4/3((3/2)^n-1))/(1/2)


    Last edited by CaptainBlack; April 7th 2011 at 06:30 AM.
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  2. #2
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    Quote Originally Posted by Rosie View Post
    Please help me with the following sum:

    Dermine n if:
    665/24=(4/3((3/2)^n-1))/(1/2)
    <br />
\frac{665}{24}<br />
=<br />
\frac<br />
{<br />
\frac{4}{3}.<br />
(\frac{3}{2})^{n-1}<br />
}<br />
{\frac{1}{2}}<br />

    <br />
\frac{665}{24}.\frac{1}{2}<br />
=<br />
\frac{4}{3}.<br />
(\frac{3}{2})^{n-1}<br />

    <br />
\frac{665}{24}.\frac{1}{2}.\frac{3}{4}<br />
=<br />
(\frac{3}{2})^{n-1}<br />

    Now take log on both sides and proceed.
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  3. #3
    Super Member Quacky's Avatar
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    Is this the problem?

    \frac{665}{24}=\frac{4}{3}(\frac{(\frac{3}{2})^n-1}{\frac{1}{2}})

    If so, how have you tried to distribute so far? Do you know that dividing by a half is the same as multiplying by 2?

    Start by dividing both sides by 4 and multiplying both sides by 3 to give:

    \frac{665}{24}\times\frac{3}{4}=\frac{(\frac{3}{2}  )^n-1}{\frac{1}{2}}

    \frac{665}{24}\times\frac{3}{4}=2\times ((\frac{3}{2})^n-1)

    I would go further, but I don't know whether this is the equation and nor do I know whether you've followed my working thus far. Can you provide any further contribution?

    Edit: whoops, was beaten to it.
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  4. #4
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    Quacky you have the right equation and the rest of your questions I do not understand.
    Can you please finish the equation because I truely do not get the right answer.
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  5. #5
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    solving Quacky's equation.

    \frac{665}{24}\times\frac{3}{4}=2\times ((\frac{3}{2})^n-1)

    <br />
\frac{665}{24}\times\frac{3}{4}\times\frac{1}{2}<br />
=<br />
(\frac{3}{2})^n-1<br />

    <br />
\frac{665}{24}\times\frac{3}{4}\times\frac{1}{2}+1<br />
=<br />
(\frac{3}{2})^n<br />

    solve LHS and take log on both sides

    <br />
log_e(\frac{665}{24}\times\frac{3}{4}\times\frac{1  }{2}+1)<br />
=<br />
n\times log_e(\frac{3}{2})<br />

    <br />
\frac{log_e(\frac{665}{24}\times\frac{3}{4}\times\  frac{1}{2}+1)}{log_e(\frac{3}{2})}<br />
=<br />
n <br />
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  6. #6
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    amul I do not know what log is, I have never used it before. I am just matric. The sum falls under series and sequences. So therefor I do not understand what you just did.
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  7. #7
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    Quote Originally Posted by Rosie View Post
    amul I do not know what log is, I have never used it before. I am just matric. The sum falls under series and sequences. So therefor I do not understand what you just did.
    ok
    \frac{665}{24}\times\frac{3}{4}\times\frac{1}{2}+1<br />
=<br />
(\frac{3}{2})^n

    when you solve LHS it solves to \frac{729}{64}

    <br />
(\frac{3}{2})^6=(\frac{3}{2})^n<br />

    since bases are equal powers are equal

    so n=6
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  8. #8
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    thank you very much, I see where I made my mistake.
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