Difference between log normal probability density values just reviewing two resources, I noticed a difference between the log normal p.d values :
One is here 

which takes the e to the power in which it contains ln(x)
the other is here

Which on page 5 , claims the same power with logarithm on the base of 10
which is correct ?
 A: In this context $\log$ means $\ln$ (i.e., a logarithm with base $e$), so the second website is probably not claiming that it is a logarithm with a base of ten.  For a logarithm with base ten you would generally use the notation $\log_{10}$.  The notation $\log$ is one of those nasty pieces of notation that is used to represent $\ln$ in some contexts and $\log_{10}$ in others, so you have to be able to spot which is meant from context.
Incidentally, the way I can tell that this is the case is that the density is wrong if this is a base ten logarithm.  If you were to define a random variable $X = 10^Y$ with $Y \sim \text{N}(\mu, \sigma^2)$ then you have:
$$\Bigg| \frac{dy}{dx} \Bigg| = \Bigg| \frac{d}{dx} \log_{10}x \Bigg| = \frac{\log_{10} e}{x},$$
so the pdf of $X$ would be:
$$p_X(x) = \frac{\log_{10} e}{x \sigma \sqrt{2 \pi}} \cdot \exp \Big( - \frac{1}{2} \Big( \frac{\log_{10} x - \mu}{\sigma} \Big)^2 \Big).$$
So you can see that if you were to define a lognormal random variable on the base-10 scale then it would have an additional scaling term $\log_{10}e$ in order to make it integrate to one. 
