I am currently reading a mathematical finance paper on option pricing. In it, the authors consider a complete probability space $(\Omega, \mathcal{F}, P)$. The paper then defines a new probability measure $Q$, which turns out to be equivalent to the original probability measure $P$. Here are the details:
$$\rho_t := \exp \left(\int\limits_0^t f(X_s)\ dW_s - \frac{1}{2}\int\limits_0^t (f(X_s))^2\ ds\right), \qquad 0 \leq t \leq T$$ where $f$ is a predictable and simple function (in the measure-theoretic sense) ($f$ is the market price of risk) and $W$ is a standard Brownian Motion w.r.t $P$. $\{\rho_t\}_t$ is an exponential martingale wrt $P$. Then $Q$ is defined as:
$$\frac{\partial Q}{\partial P} := \rho_T$$ After this, the paper states that $Q$ is equivalent to $P$. How can I prove this? I know that two measures are equivalent if they are both absolutely continuous w.r.t each other. I don't know how to use this definition to prove equivalence here.