How to convert this exponential equation to linear equation.
$Y =\exp(17.9348)\cdot x^{-2.705}$
what I did is:
$Y =\log(17.9348)-2.705\log(x).$
I am confused with this one:
$Y=17.9348-2.705\log(x).$
Which one is correct transformation?
Thanks in advance!
Best Answer
The answer is neither! You need to take the logarithm of both sides: \begin{align*} y&=e^{17.9348}\,x^{-2.705} \\ \ln(y)&=\ln\left(e^{17.9348}\,x^{-2.705}\right) \\ \ln(y)&=\ln\left(e^{17.9348}\right)+\ln\left(x^{-2.705}\right) \\ \ln(y)&=17.9348-2.705\ln(x). \end{align*}