Consider a random variable $X$ with the log-normal pdf $f(x) ={1\over \sqrt{2π}}x^{−1}e^{{−0.5 (logx)^2}}$, $x >0$.
Show how to form a location-scale family $g(x)$ based on $f(x)$ such that $g(x)$ has mean $0$ and variance $1$.
I'm not sure how to go about this. I know that a location-scale family is a family of probability distributions parametrized by a location parameter and a non-negative scale parameter.