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  "body": "\n## Statement\n\nFor all real $x \u003e 0$ and $y \u003e 0$,\n$$\\ln(x y) = \\ln x + \\ln y.$$\n\n## Remarks\n\nBy [[the sum rule for exp|0E8HNVBCSP]], $e^{\\ln x + \\ln y} = e^{\\ln x} e^{\\ln y} = x y$. Now [[take logarithms|0RKW2X63YR]].\nSo $\\ln$ is a group isomorphism from $((0, \\infty), \\cdot)$ to $(\\mathbb{R}, +)$.\nMathlib states it as `Real.log_mul`, for nonzero $x$ and $y$.\n\n## Explanations\n\n### L1 human\n\nThe logarithm turns multiplication into addition.\nThis property made logarithm tables useful for hand computation.\n",
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