Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

My maths is not very good, so please bare with me if the answer is obvious. I have a log-log plot below, which I have generated in R.

enter image description here

I now need to find what i believe to be called the inverse to the function of the plot, resulting in me obtaining the following equation:

$y = constant . x^m$

I understand that $m$ will be the gradient of the line (0.71), but how do I calculate the constant?

share|improve this question

1 Answer 1

up vote 2 down vote accepted

CORRECTION (the constant factor depends of the $\log$ basis considered!) :

If $\log$ means $\log_{10}$ on both axis then

you got $\ \log_{10}(y)=5.3+0.71\log_{10}(x)\ $ (since $\ \log_{10}\bigl(x^{0.71}\bigr)=0.71\;\log_{10}(x)$).

Take the 'antilog' $10^x$ to obtain $\ y\approx 10^{5.3}\ x^{0.71}$ or : $$\boxed{y\approx 200000\ x^{0.71}}$$ (because $\log_{10}(2)\approx 0.3$ and with $2$ digits precision)

else if the 'natural logarithm' i.e. $\ln$ was taken on both sides then :

You got $\ \ln(y)=5.3+0.71\ln(x)$.

take the exponential of this to obtain $\ y\approx e^{5.3}\ x^{0.71}$ or : $$\boxed{y\approx 200\ x^{0.71}}$$

(because $\,e^{a+b}=e^a e^b\,$ and $\,x^c= e^{c\ln(x)}$)

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.