Preimage resistance hash in digital signature I'm studying about preimage resistance property of the hash functions.
In particularly I'm reading as the missing of this property can be fatal in digital signatures that use RSA.

Further details:

Let $e$ be the public exponent, $d$ the private exponent and $n$ the modulus.

Let be C the attacker.

C could compute:

$y= z^e \mod n$
with $z$ random number, then he could find a $m'$ for the which $h(m') = y$ and finally
to state that Bob has sent {$m'$, $z$} where $m'$ is the message and $z$ is the digital signature.

Here my doubts:

C could choose $m'$ if he could compute:
$h(m') = y$ (the compute is easy, suppose that h is public) and resolve this equation;
$\log_x y = e$ (there is also $\mod n$ in this equation).
This problem seems similar to discrete logarithm but it is different.
In this case the unknown is the logarithm base.

I think that this problem is computationally intractable, do you confirm?
I'm having a hard time parsing your question.

If C can compute pre-images on $H$, then he can forge digital signatures from Bob. All C needs is one signature from Bob.

Bob signs message $m$, the signature is $S={H(m)}^d\bmod n$. All C needs to do is find an $m'$ where $H(m)=H(m')$. The forged message and signature will be $m'$ and the original $S$.