= Solution
For an approximately scale-invariant primordial spectrum, the late <cosmological density power spectrum> behaves schematically as
$$
P(k)\propto k^{n_s}T^2(k).
$$
Modes with $k\ll k_{\rm eq}$ enter the horizon after matter-radiation equality and retain $T(k)\simeq1$, so $P(k)\sim k^{n_s}$. Modes with $k\gg k_{\rm eq}$ enter during radiation domination and grow only logarithmically until equality. Their transfer function behaves as $T(k)\sim\log(k/k_{\rm eq})/(k/k_{\rm eq})^2$, giving a strongly falling small-scale spectrum. The result is a turnover near the <matter-radiation equality scale> $k_{\rm eq}$.
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