[Interactive Graph] Add logarithm math utilities to kmath

[ivyolamit]

Summary:

PR series to add logarithm graph support to the Interactive Graph widget:

1. Add logarithm graph type definitions and data
2. ▶️ Add logarithm math utilities to kmath
3. Add logarithm graph state management and reducer
4. Add logarithm graph rendering, SR strings, and equation string
5. Add logarithm graph scoring
6. Add logarithm graph option in the Interactive Graph Editor

Add the logarithm math utilities to kmath for supporting Logarithm graph in Interactive Graph

• Add LogarithmCoefficient type and getLogarithmCoefficients() to kmath, following the exponential pattern
• Compute coefficients {a, b, c} for f(x) = a·ln(b·x + c) using the inverse exponential approach
• No canonical normalization needed (logarithm has no periodic equivalences, same as exponential)

Details

This adds the shared math utility for logarithm coefficient computation to @khanacademy/kmath, following the same pattern as getExponentialCoefficients(). Both the rendering component (PR 4) and scoring (PR 5) will consume this function.

Mathematical approach (inverse exponential):

1. Flip each coordinate (x, y) → (y, x) — treating the logarithm as the inverse of an exponential
2. Use the asymptote x-value as the flipped exponential's c coefficient
3. Compute exponential coefficients aExp, bExp from the flipped points
4. Invert to get logarithm coefficients: a = 1/bExp, b = 1/aExp, c = -cExp/aExp

Validation guards (returns undefined for invalid inputs):

• Same y-coordinate on both points (makes bExp undefined)
• A point lying on the asymptote
• Points on opposite sides of the asymptote
• Non-finite or zero intermediate results

This matches the reference implementation in packages/perseus-core/src/utils/grapher-util.ts (the Grapher widget's Logarithm object, lines 449–558).

Co-Authored by Claude Code (Opus)

Issue: LEMS-3953

Test plan

• pnpm tsc passes
• pnpm knip passes
• pnpm lint passes
• pnpm prettier . --check passes
• Coefficient tests pass (6 new tests, 17 total in coefficients.test.ts)
• Grapher test data: [-4,-3], [-5,-7], asymptote -6 reproduces correct y-values
• Natural log: [1,0], [e,1], asymptote 0 → a≈1, b≈1, c≈0
• Negative b: points left of asymptote (y = ln(-x)) → b≈-1
• Same-y → undefined
• Point on asymptote → undefined
• Opposite sides → undefined

[github-actions]

🗄️ Schema Change: No Changes ✅

[github-actions]

🛠️ Item Splitting: No Changes ✅

[github-actions]

Size Change: +134 B (+0.03%)

Total Size: 495 kB

Filename	Size	Change
packages/kmath/dist/es/index.js	6.35 kB	+134 B (+2.16%)

ℹ️ View Unchanged

Filename	Size
packages/kas/dist/es/index.js	20.5 kB
packages/keypad-context/dist/es/index.js	1 kB
packages/math-input/dist/es/index.js	98.5 kB
packages/math-input/dist/es/strings.js	1.61 kB
packages/perseus-core/dist/es/index.item-splitting.js	12 kB
packages/perseus-core/dist/es/index.js	25.2 kB
packages/perseus-editor/dist/es/index.js	101 kB
packages/perseus-linter/dist/es/index.js	9.3 kB
packages/perseus-score/dist/es/index.js	9.66 kB
packages/perseus-utils/dist/es/index.js	403 B
packages/perseus/dist/es/index.js	193 kB
packages/perseus/dist/es/strings.js	8.09 kB
packages/pure-markdown/dist/es/index.js	1.39 kB
packages/simple-markdown/dist/es/index.js	6.71 kB

_{compressed-size-action}

[github-actions]

npm Snapshot: Published

Good news!! We've packaged up the latest commit from this PR (48b121b) and published it to npm. You
can install it using the tag PR3421.

Example:

pnpm add @khanacademy/perseus@PR3421

If you are working in Khan Academy's frontend, you can run the below command.

./dev/tools/bump_perseus_version.ts -t PR3421

If you are working in Khan Academy's webapp, you can run the below command.

./dev/tools/bump_perseus_version.js -t PR3421

[ivyolamit]

@claude review

[claude]

LGTM — clean, well-tested math utility following the existing exponential pattern.

Extended reasoning...

Overview

Adds LogarithmCoefficient type and getLogarithmCoefficients() to packages/kmath/src/coefficients.ts, exports the type in index.ts, and adds a changeset file. 4 files changed, all additive.

Mathematical correctness

The inverse-exponential derivation is sound. For f(x) = a·ln(b·x + c), flipping coordinates transforms the problem into fitting an exponential x = aExp·e^(bExp·y) + cExp where cExp = asymptote. Inverting gives a = 1/bExp, b = 1/aExp, c = -cExp/aExp — all verified algebraically. The validation guards (same-y, point on asymptote, opposite sides, non-finite/zero intermediates) correctly cover degenerate cases, including the extra bExp === 0 guard needed because a = 1/bExp.

Security risks

None. This is a pure math utility with no I/O or user-input handling.

Level of scrutiny

Low. The change is additive-only, follows an established pattern (getExponentialCoefficients), and all checks passed (tsc, lint, prettier, knip). The 6 new tests exercise both happy paths and all four error/invalid-input cases.

Other factors

No CODEOWNERS concerns for this kmath utility file. Bundle impact is +134 B, as expected.

[claude]

Claude Code Review

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[SonicScrewdriver]

Looks great to me! The graph appears to work well when I manually test as well