rearrange exponential equation y = c*e^(b*x) for x

[bananabunny]

hi there,
i have graphed some data in excel and i have fit an exponential trendline. i am unsure how to rearrange the equation which is in the form of y = c*e^(b*x). i know that b and c are constants and these numbers have been given to me but i am not sure how to rearrange this equation for x. i can't quite remember the rules for e and logarithms and i'm not sure where to start. any help would be very much appreciated.

 

[Jose.]

Hello

\(\displaystyle y/c=e^{bx}\) then you take logarithms in both sides and you have \(\displaystyle bx=log(y/c)\); \(\displaystyle x=(1/b)log(y/c)\);

\(\displaystyle x=log{(y/c)^{1/b}} \)

where \(\displaystyle log(x)\) is the natural logarithm and I used \(\displaystyle log(e^{bx})=bx\)