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I'm trying to solve the equation $$\zeta'(x)/\zeta(x) = - 3/4$$ numerically. I'm expecting/hoping for an answer between 1 and 10.

I tried

$\texttt{ find_root(diff(zeta(x))/zeta(x) + 0.75, 2, 40)}$,

but this returns 0.0. I don't know what that ratio of zeta functions looks like, so it's possible there isn't a root, but I don't see why I'm getting an answer outside the specified interval.

Can anyone help find the true root? Thanks.