= Solution
Comparing <photons> with the constant vacuum density gives $\Omega_{\gamma0}(1+z)^4=0.7$, so
$$
\boxed{z_{\gamma\Lambda}=\left(\frac{0.7}{4.8032\times10^{-5}}\right)^{1/4}-1\simeq9.98735}.
$$
Matter dominates both at this crossing: its density in units of today's <critical density> is $0.3(10.98735)^3\simeq398$, compared with $0.7$ for each of the other components. <radiation-vacuum density equality> therefore does not itself mark a switch in the dominant component.
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