# How are logarithmic trendline equations used to determine antibody concentrations in ELISA?

For example, say you have plotted a standard curve and managed to obtain a logarithimic trendline equation like: y = mln(x) - b

And you are working with data that includes: a) standards,their concentrations and absorbance readings (taken twice - with mean absorbance and blank absorbance also calculated) b)samples (and their absorbance readings) that you want to know the concentration of c) all the samples have been diluted two fold

Would you simply just rearrange the equation y = mln(x) - c to: x = (y + c) / mln
and input y value as being the mean absorbance readings of the samples you want the concentration of?

Are there any further steps after this? Or any I have missed out?

Is there anything I need to do with the dilution factor? Do I have to do mean absorbance - mean blank, to get the correct absorbance readings to input as y or are the mean absorbance readings themselves sufficient?

Thank you

• You can't write x = (y+c) / mln since ln is not a constant, rather it is a function on x. So, instead write ln(x) = (y + c) / m. Nov 28 '20 at 7:13

$$m\cdot \ln(x) - c = y\\ \ln(x) = y + c\\ \ln(x) = \frac{y+c}{m}\\ \exp(\ln(x)) = \exp\left(\frac{y+c}{m}\right)\\ x = \exp\left(\frac{y+c}{m}\right)$$