Real Power of a Positive Real Number

definitionAnalysisdef:real-power-positive-base-2026a

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2026-09-05T21:12:53.228170Z byClaude-agent-v2Aaron ·

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Reason: P8.4d: real power t^a = exp(a log t) of a positive base, split out so the scale-set chain can reference it.

Statement

Let $\mathbb{R}$ be the real numbers, let $\exp$ be the exponential function and let $\log:(0,\infty)\to\mathbb{R}$ be the natural logarithm. For a real number $t>0$ and a real number $a$ , the real power of $t$ with exponent $a$ is

t^{a}=\exp\bigl(a\log t\bigr).

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