Does this distribution belong to the exponential class

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I've come across a following problem:

$$ f(x; \mu, \sigma^2) = e^{\frac{1}{2 \sigma^2}(ln x - \mu)^2}, \quad x>0 $$

Does this distribution belong to the exponential class?

To be honest, I have no idea how to show that...

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This is called Log-normal distribution.