# Zero knowledge proof of equality of discrete log and hash preimage

So my question is as follows: We know that we can prove in zero-knowledge equality of discrete logs, for example to prove equality of committed values we can prove in ZK for $$g^xh^y$$ and $$g^{x'}h^{y'}$$ that $$x = x'$$ using a Sigma protocol.

Is there a way to prove equality when one committed value is the output of a hash function? This means prove in ZK for $$g^xh^y$$ and $$H(x')$$ that $$x = x'$$. (the tricky part here is that the Hash function doesn't necessarily have homomorphic properties as the commitment does)