Re-arranging with natural logs to different powers

Question

I am trying to rearrange the equation $$T=\frac{1}{A+B\cdot \ln(R)+C\cdot \ln(R)^3}$$ Where $A, B\space and\space C$ are constants and $R$ is the independent variable. I would like to get an equation where $T$ is the independent variable. I know the steps up to $$\frac{1}{T}-A=B\cdot\ln(R)+C\cdot\ln(R)^3$$ But I do not know how to proceed any further. Thank you in advance for the help.

Is that $[\ln R]^3$ or $\ln(R^3)$? – fleablood Oct 15 '19 at 02:57 — fleablood, Oct 15 '19 at 02:57

score 1 · Accepted Answer · answered Oct 15 '19 at 02:56

1

$\frac{1}{T}-A=B\cdot\ln(R)+C\cdot\ln(R)^3$

$= B\ln R + 3C\ln R = \ln R(B+3C)$

so

$\frac {\frac 1T -A}{B+3C} = \ln R$

So

$R = e^{\frac {\frac 1T -A}{B+3C}}$

answered Oct 15 '19 at 02:56

fleablood

124,253

The other case would be more funny ! – Claude Leibovici Oct 15 '19 at 04:36

Re-arranging with natural logs to different powers

1 Answers1