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Logs question? (C4)

How do you make T the subject in this equation?

ln2 + (T-10)lnp = Tlnq
Reply 1
Avatar for Zacken
Zacken
22
Original post by Phoebus Apollo
How do you make T the subject in this equation?

ln2 + (T-10)lnp = Tlnq


First put evverything involving T one one side, so:

Unparseable latex formula:

\displaystyle[br]\begin{align*} \ln 2 + T \ln p - 10 \ln p = T \ln q & \iff T \ln q - T \ln p = \ln 2 - 10 \ln p \\ & \iff T(\ln q - \ln p) = \ln 2 - 10 \ln p\\ & \Rightarrow \cdots \end{align*}



You can simplify using the addition/subtractin rules for logarithms, i.e: ln⁡q−ln⁡p=ln⁡qp\ln q - \ln p = \ln \frac{q}{p}. Then divide by the coefficient of TT to get it alone.
Original post by Phoebus Apollo
How do you make T the subject in this equation?

ln2 + (T-10)lnp = Tlnq


Next step: ln2 + T*lnp - 10*lnp = Tlnq
then, T*lnq + T*lnp = ln2 + 10*lnp
so, T*ln(q/p) = -ln(10^p/2)
finally, T= -ln(10^p/2) / ln(q/p)
(edited 7 years ago)
misread
Reply 4
Avatar for Zacken
Zacken
22
Original post by Bath~Student
Next step: ln2 + T*lnp - 10*lnp = Tlnq
then, T*lnq - T*lnp = ln2 + 10*lnp
so, T*ln(q/p) = ln(10^p/2)
finally, T= ln(10^p/2) / ln(q/p)


Bolded the incorrect bits.
Original post by Zacken
Bolded the incorrect bits.


Oh, that's disgusting.



That's what comes from trying to beat you, that one addicted, self-declared genius who dwells here, day and night.
Reply 6
Avatar for Zacken
Zacken
22
Original post by Bath~Student
Oh, that's disgusting.

That's what comes from trying to beat you, that one addicted, self-declared genius who dwells here, day and night.


Cheers.
Original post by Zacken
First put evverything involving T one one side, so:

Unparseable latex formula:

\displaystyle[br]\begin{align*} \ln 2 + T \ln p - 10 \ln p = T \ln q & \iff T \ln q - T \ln p = \ln 2 - 10 \ln p \\ & \iff T(\ln q - \ln p) = \ln 2 - 10 \ln p\\ & \Rightarrow \cdots \end{align*}



You can simplify using the addition/subtractin rules for logarithms, i.e: ln⁡q−ln⁡p=ln⁡qp\ln q - \ln p = \ln \frac{q}{p}. Then divide by the coefficient of TT to get it alone.


Original post by Bath~Student
Next step: ln2 + T*lnp - 10*lnp = Tlnq
then, T*lnq + T*lnp = ln2 + 10*lnp
so, T*ln(q/p) = -ln(10^p/2)
finally, T= -ln(10^p/2) / ln(q/p)


Thanks!

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