Why log returns are used in finance: they add across time, so multi-period returns are sums rather than products, and sums are what the central limit theorem applies to. That single property is why price models are built on log returns.
Approximations worth memorising: ln(1+x) ≈ x for small x, so a 1% return and a 1% log return are nearly identical - but they diverge for large moves, which is where volatility drag comes from.
Anchors: ln 2 ≈ 0.693, log10(2) ≈ 0.301, which means 2^10 ≈ 10^3.