# Logarithms – Using Log Data for Parameter Estimation

Say I have data as a $$x_1, x_2, .. x_n$$ and I adapt a model to these data for example, $$Y (t) = Y_0 e ^ {- lambda t}$$. I'm trying to estimate the parameter $$lambda$$ adjusting to these data.
In these estimation procedures, I do not quite understand what is the use of the logarithmic data for the estimation of parameters?

Does the use of log data have an advantage when the data varies over a wide range, such as $$10 ^ 7$$ at $$1$$

1. When using data without transformation,

``````    model = @ (x, t) data (1) * exp (x (1). * t);

[lambda,error]= lsqcurvefit (model, initial, t, data);
``````
2. If I use the log data, I'll call the function like,

``````    model = @ (x, t) log10 (data (1)) * exp (x (1). * t);

[lambda,error]= lsqcurvefit (model, initial, t, log10 (data));
``````

Thus, the model itself does not change and only the logarithm of the data is taken.

Is there a relationship between the $$lambda$$ value I get from the 2 methods above?

In addition, which one is the right one $$lambda$$ value?

When using log data, should the entire model also be transformed, so that I am able to $$log (Y) = log (Y_0) – lambda t$$
or can I just use the data log while the model remains unchanged?