How Do I Calculate the Variance of a Transformed Random Variable?

[MaxManus]

Homework Statement

How do I calculate the variance of
$$\frac{1}{\log{X} + 2}$$

where X is a random variable?

The Attempt at a Solution

Is it:
$$\frac{1}{\log{var(X)}}$$

Homework Equations

The Attempt at a Solution

 

[planck42]

What is the expectation value of the probability distribution?

 

[MaxManus]

The forst post was just something I made up. The estimator I am trying to calculate the variance of:
$$\hat{\theta} = \frac{n}{\sum{ln(X_i)}_{i=1}^n - n \ln(k)}$$

Which is the maximum likelihood to a pareto distribution
When I calculated the expected value I got:

$$E(\hat{\theta}) = \frac{\theta}{\theta-1}$$
$$E(X) = \frac{\theta k}{\theta - 1}$$