1. ## rearranging log function

Hi all..

I wanted to know how to rearrange the following to get S as subject, just bit confused on what to do with the Clog mulitplying the S

K = logT + ClogS

Thank you

Hi all..

I wanted to know how to rearrange the following to get S as subject, just bit confused on what to do with the Clog mulitplying the S

K = logT + ClogS

Thank you
I assume that $\displaystyle \log$ means $\displaystyle \log_{10}$.

If so:

$\displaystyle K=\log(T) +C \cdot \log(S)=\log(T \cdot S^C)$

Now use the base 10:

$\displaystyle 10^K= T \cdot S^C ~\implies~\boxed{S=\sqrt[C]{\dfrac{10^K}{T}}}$

3. Originally Posted by earboth
I assume that $\displaystyle \log$ means $\displaystyle \log_{10}$.

If so:

$\displaystyle K=\log(T) +C \cdot \log(S)=\log(T \cdot S^C)$

Now use the base 10:

$\displaystyle 10^K= T \cdot S^C ~\implies~\boxed{S=\sqrt[C]{\dfrac{10^K}{T}}}$
Thanks for the help. Nicely explained

The "ClogS" is the product of the variable "C" and the logarithmic function of S; that is, "ClogS" means $\displaystyle C\times\log(S)$, not $\displaystyle Clog\times S$