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Re arranging formula

  1. Mar 16, 2009 #1
    Hi, could any one show me how to make T the subject?

    V*T to the power n = C

    Thanks
     
  2. jcsd
  3. Mar 16, 2009 #2

    CompuChip

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    If
    [tex]T^n = c[/tex]
    then
    [tex](T^n)^{1/n} = T = c^{1/n}[/tex]
     
  4. Mar 16, 2009 #3
    Thanks compu, could you just explain the rule as to why it is C^1/n?

    Thanks James
     
  5. Mar 16, 2009 #4
    If n=0.3 Then T^3/10 so C would be the 10 root of C to the power of 3. Is that right? or am i getting my indices and power rules wrong?
    Thanks for any help offerd

    James
     
  6. Mar 16, 2009 #5
    Knowing that the logarithm of x^n is n times the logarithm of x:

    [tex]VT^{n}=C[/tex]

    [tex]T^{n}=\frac{C}{V}[/tex]

    [tex]log \left[ T^{n} \right] = log \left[ \frac{C}{V} \right] [/tex]

    [tex]n log \left[ T \right] = log \left[ \frac{C}{V} \right] [/tex]

    [tex]log \left[ T \right] = \frac{1}{n} log \left[ \frac{C}{V} \right] [/tex]

    [tex]log \left[ T \right] = log \left[ \left( \frac{C}{V} \right)^{\frac{1}{n}} \right] [/tex]

    [tex]T = \left( \frac{C}{V} \right)^{\frac{1}{n}} [/tex]

    Many thanks to all for bracket help.
     
    Last edited: Mar 17, 2009
  7. Mar 16, 2009 #6
    Thanks Timmay. Great explanation. Just a couple of things i don't get. Why is nLog(T)=Log(c/v) then become log (T)=1/nlog(c/v). And why is not just T^n=c becomes T=nroot of c?

    Thanks for all your reply's a great help James
     
  8. Mar 17, 2009 #7

    CompuChip

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    Because if AB=C then B=C/A?
    I.e. primary school algebra :wink:

    It is. Raising something to the power 1/n is the same as taking the n-th root (cf. a^(1/2) = sqrt(a) = 2root(a)).

    [Just realized what the confusion might be: note that my c is not your C... you first have to rewrite V T^n = C to T^n = c to apply what I said. ]
     
  9. Mar 17, 2009 #8

    minger

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    Try
    Code (Text):

    \left( ..... \right)
     
    Rather than simply (...). \left[ \right] also works :)
     
  10. Mar 17, 2009 #9

    CompuChip

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    Like this:
    [tex]\left\{ \log\left[ \left(\frac{\left( C \right)}{V} \right)^{\frac{1}{n}} \right] \right\}[/tex]

    (click to see the source)
     
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