initial commit

_bmad-output/implementation-artifacts/6-2-logarithmic-and-exponential-functions.md

@@ -0,0 +1,69 @@
+---
+epic: 6
+story: 6.2
+title: "Logarithmic & Exponential Functions"
+status: draft
+---
+
+## Epic 6 — Advanced Math & Functions
+**Goal:** Scientific, financial, and power-user math.
+
+### Story 6.2: Logarithmic & Exponential Functions
+
+As a **CalcPad user**,
+I want to use logarithmic and exponential functions including ln, log, log2, exp, pow, sqrt, cbrt, and nth-root,
+So that I can perform scientific, financial, and engineering calculations involving growth, decay, and roots.
+
+**Acceptance Criteria:**
+
+**Given** the user writes `ln(1)`
+**When** the engine evaluates
+**Then** the result is `0`
+
+**Given** the user writes `ln(e)` where `e` is Euler's number
+**When** the engine evaluates
+**Then** the result is `1`
+
+**Given** the user writes `log(100)`
+**When** the engine evaluates
+**Then** the result is `2` (base-10 logarithm)
+
+**Given** the user writes `log2(256)`
+**When** the engine evaluates
+**Then** the result is `8`
+
+**Given** the user writes `exp(1)`
+**When** the engine evaluates
+**Then** the result is approximately `2.71828` (e^1)
+
+**Given** the user writes `2^10`
+**When** the engine evaluates
+**Then** the result is `1024`
+
+**Given** the user writes `pow(2, 10)`
+**When** the engine evaluates
+**Then** the result is `1024`
+
+**Given** the user writes `e^3`
+**When** the engine evaluates
+**Then** the result is approximately `20.0855`
+
+**Given** the user writes `sqrt(144)`
+**When** the engine evaluates
+**Then** the result is `12`
+
+**Given** the user writes `cbrt(27)`
+**When** the engine evaluates
+**Then** the result is `3`
+
+**Given** the user writes an nth-root expression such as `4th root of 625` or `root(625, 4)`
+**When** the engine evaluates
+**Then** the result is `5`
+
+**Given** the user writes `ln(0)` or `log(-1)`
+**When** the engine evaluates
+**Then** the engine displays an error indicating the argument is out of the valid domain
+
+**Given** the user writes `sqrt(-4)`
+**When** the engine evaluates
+**Then** the engine displays an error (complex numbers are out of scope unless explicitly supported)