# BoxCox transformation suggest natural logarithm transformation. Can log10 transformation be used instead? [duplicate]

I run a Box-Cox transformation for a linear model to find an appropriate transformation for a response variable, which is a number of insect per sq.meter. I need to transform the response variable because of a pattern in the residual plot obtained after running the linear regression using none-transformed response variable. I used a boxcox() function from the ‘MASS’ package in R. Box-Cox suggested the best lambda value of 0.055 for transformation, which is close to 0 and corresponds to natural log transformation (Osborne 2010).

My question is may I use log10 transformation instead of natural log transformation? log10 transformation is the most common transformation my field. Are there any references, to back up this decision?

Just to mention, I can’t use Poisson regression because I work with averaged values of insects per sq.m, it is complications of using different sampling equipment.

Thanks

## marked as duplicate by Glen_b♦Sep 5 '16 at 23:38

Yes, you can! All logarithms are proportional, so the results will be identical, the proportionality constant will just change the estimated coefficients. Too see this: $$y = \log_e x ~~\text{then} \\ e^y = x ~~\text{and then} \\ \log_{10} x = \log_{10} (e^y) = y \cdot \log_{10} e \approx 0.434 \cdot y$$ so estimated coefficients will change only by that constant $0.434$, the fit of the model will be identical, and hypothesis tests and so on will give identical results.