# Log and natural log

I have few seemingly simple questions.

1. I am working on time series data and applying vector error correction model. I find different results when I transform the data into LOG and LN. Which one is better?

2. I have variables in % and in levels (numbers). I have for example one which is measured in million USD and others in %. My question: shall I list the whole number in eviews like 47,000,000,000 or just 47 and then bring in the billion when interpreting the results? Does it make any difference when running Johansen's test?

• That is at least two questions. For (1): $\ln(x) \approx 2.302585\times \log_{10}(x)$ so the only impact should be that of a scaling factor – Henry Jun 9 '14 at 22:52

1) We have that $\log_a y = \frac{\ln y}{\ln a}$ so the only effect of the difference is that of a scale factor.