diff --git a/.changeset/famous-ears-mix.md b/.changeset/famous-ears-mix.md
new file mode 100644
index 00000000000..ff3b834e070
--- /dev/null
+++ b/.changeset/famous-ears-mix.md
@@ -0,0 +1,6 @@
+---
+"@khanacademy/perseus": minor
+"@khanacademy/perseus-editor": minor
+---
+
+Add logarithm graph option in the Interactive Graph Editor
diff --git a/packages/perseus-editor/src/widgets/interactive-graph-editor/components/graph-type-selector.tsx b/packages/perseus-editor/src/widgets/interactive-graph-editor/components/graph-type-selector.tsx
index bbb8324530b..610c90fbe84 100644
--- a/packages/perseus-editor/src/widgets/interactive-graph-editor/components/graph-type-selector.tsx
+++ b/packages/perseus-editor/src/widgets/interactive-graph-editor/components/graph-type-selector.tsx
@@ -29,6 +29,11 @@ const GraphTypeSelector = (props: GraphTypeSelectorProps) => {
         "interactive-graph-tangent",
     );
 
+    const showLogarithm = isFeatureOn(
+        {apiOptions: props.apiOptions},
+        "interactive-graph-logarithm",
+    );
+
     return (
         <SingleSelect
             selectedValue={props.graphType}
@@ -49,6 +54,9 @@ const GraphTypeSelector = (props: GraphTypeSelectorProps) => {
             {showTangent && (
                 <OptionItem value="tangent" label="Tangent function" />
             )}
+            {showLogarithm && (
+                <OptionItem value="logarithm" label="Logarithm function" />
+            )}
             <OptionItem value="circle" label="Circle" />
             <OptionItem value="point" label="Point(s)" />
             <OptionItem value="linear-system" label="Linear System" />
diff --git a/packages/perseus-editor/src/widgets/interactive-graph-editor/interactive-graph-editor.tsx b/packages/perseus-editor/src/widgets/interactive-graph-editor/interactive-graph-editor.tsx
index 2ca971f3833..a9345a86a7b 100644
--- a/packages/perseus-editor/src/widgets/interactive-graph-editor/interactive-graph-editor.tsx
+++ b/packages/perseus-editor/src/widgets/interactive-graph-editor/interactive-graph-editor.tsx
@@ -285,6 +285,25 @@ class InteractiveGraphEditor extends React.Component<Props> {
             }
         }
 
+        // Logarithm: the start asymptote must not fall between or on the
+        // curve's start points — that configuration produces an invalid
+        // logarithm (the coefficient formula requires all points to be
+        // strictly on one side of the asymptote).
+        if (
+            this.props.graph?.type === "logarithm" &&
+            this.props.graph.startCoords != null
+        ) {
+            const {coords, asymptote} = this.props.graph.startCoords;
+            const asymptoteX = asymptote;
+            const minX = Math.min(coords[0][0], coords[1][0]);
+            const maxX = Math.max(coords[0][0], coords[1][0]);
+            if (asymptoteX >= minX && asymptoteX <= maxX) {
+                issues.push(
+                    "The logarithm start asymptote must not fall between or on the curve's start points.",
+                );
+            }
+        }
+
         return issues;
     };
 
diff --git a/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/start-coords-logarithm.module.css b/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/start-coords-logarithm.module.css
new file mode 100644
index 00000000000..8821417a1fc
--- /dev/null
+++ b/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/start-coords-logarithm.module.css
@@ -0,0 +1,36 @@
+/* We have to use !important until wonder blocks is in the shared layer. */
+/* TODO(LEMS-3686): Remove the !important once we don't need it anymore. */
+.tile {
+    background-color: var(
+        --wb-semanticColor-core-background-instructive-subtle
+    ) !important;
+    margin-top: var(--wb-sizing-size_080) !important;
+    padding: var(--wb-sizing-size_120) !important;
+    border-radius: var(--wb-sizing-size_080) !important;
+}
+
+.row {
+    display: flex !important;
+    flex-direction: row !important;
+    align-items: center !important;
+}
+
+.textFieldWrapper {
+    width: var(--wb-sizing-size_800) !important;
+}
+
+.equationSection {
+    margin-top: var(--wb-sizing-size_120) !important;
+}
+
+.equationBody {
+    background-color: var(
+        --wb-semanticColor-core-background-neutral-subtle
+    ) !important;
+    border: var(--wb-border-width-thin) solid
+        var(--wb-semanticColor-core-border-neutral-subtle) !important;
+    margin-top: var(--wb-sizing-size_080) !important;
+    padding-left: var(--wb-sizing-size_080) !important;
+    padding-right: var(--wb-sizing-size_080) !important;
+    font-size: var(--wb-font-size-xSmall) !important;
+}
diff --git a/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/start-coords-logarithm.tsx b/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/start-coords-logarithm.tsx
new file mode 100644
index 00000000000..03ca2d6f52b
--- /dev/null
+++ b/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/start-coords-logarithm.tsx
@@ -0,0 +1,118 @@
+import {View} from "@khanacademy/wonder-blocks-core";
+import {Strut} from "@khanacademy/wonder-blocks-layout";
+import {spacing} from "@khanacademy/wonder-blocks-tokens";
+import {BodyMonospace, BodyText} from "@khanacademy/wonder-blocks-typography";
+import * as React from "react";
+
+import CoordinatePairInput from "../../../components/coordinate-pair-input";
+import ScrolllessNumberTextField from "../../../components/scrollless-number-text-field";
+
+import styles from "./start-coords-logarithm.module.css";
+import {getLogarithmEquation} from "./util";
+
+import type {Coord} from "@khanacademy/perseus";
+
+type LogarithmStartCoords = {
+    coords: [Coord, Coord];
+    asymptote: number;
+};
+
+type Props = {
+    startCoords: LogarithmStartCoords;
+    onChange: (startCoords: LogarithmStartCoords) => void;
+};
+
+const StartCoordsLogarithm = (props: Props) => {
+    const {startCoords, onChange} = props;
+    const {coords, asymptote} = startCoords;
+
+    // Local state for the asymptote x-value text field so the user can type
+    // freely without the field resetting mid-keystroke. Pattern from StartCoordsCircle.
+    const [asymptoteXState, setAsymptoteXState] = React.useState(
+        asymptote.toString(),
+    );
+
+    // Sync local state when props change (e.g. "Use default start coordinates" button).
+    React.useEffect(() => {
+        setAsymptoteXState(asymptote.toString());
+    }, [asymptote]);
+
+    function handleAsymptoteXChange(newValue: string) {
+        // Update the local state to update the input field immediately.
+        setAsymptoteXState(newValue);
+
+        // Assume the user is still typing. Don't update props until a valid number.
+        if (isNaN(+newValue) || newValue === "") {
+            return;
+        }
+
+        // Update the props (updates the graph).
+        const newX = parseFloat(newValue);
+        // Spread coords into a new array so that startCoords always gets a
+        // new reference. StatefulMafsGraph's useEffect only watches startCoords,
+        // so a new reference is required to trigger reinitialization even when
+        // only the asymptote changes. (Same reason circle creates a new
+        // {center, radius} object on every onChange call.)
+        onChange({
+            coords: [coords[0], coords[1]],
+            asymptote: newX,
+        });
+    }
+
+    return (
+        <>
+            {/* Current equation */}
+            <View className={styles.equationSection}>
+                <BodyText>Starting equation:</BodyText>
+                <BodyMonospace className={styles.equationBody}>
+                    {getLogarithmEquation(coords, asymptote)}
+                </BodyMonospace>
+            </View>
+
+            {/* Points UI */}
+            <View className={styles.tile}>
+                {/* Point 1 */}
+                <View className={styles.row}>
+                    <BodyText weight="bold">Point 1:</BodyText>
+                    <Strut size={spacing.small_12} />
+                    <CoordinatePairInput
+                        coord={coords[0]}
+                        labels={["x", "y"]}
+                        onChange={(value) =>
+                            onChange({coords: [value, coords[1]], asymptote})
+                        }
+                    />
+                </View>
+                <Strut size={spacing.small_12} />
+
+                {/* Point 2 */}
+                <View className={styles.row}>
+                    <BodyText weight="bold">Point 2:</BodyText>
+                    <Strut size={spacing.small_12} />
+                    <CoordinatePairInput
+                        coord={coords[1]}
+                        labels={["x", "y"]}
+                        onChange={(value) =>
+                            onChange({coords: [coords[0], value], asymptote})
+                        }
+                    />
+                </View>
+                <Strut size={spacing.small_12} />
+
+                {/* Asymptote x-value — single number, mirroring radius in StartCoordsCircle */}
+                <BodyText weight="bold" tag="label" className={styles.row}>
+                    Asymptote x =
+                    <Strut size={spacing.small_12} />
+                    <View className={styles.textFieldWrapper}>
+                        <ScrolllessNumberTextField
+                            value={asymptoteXState}
+                            onChange={handleAsymptoteXChange}
+                        />
+                    </View>
+                </BodyText>
+            </View>
+        </>
+    );
+};
+
+export default StartCoordsLogarithm;
diff --git a/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/start-coords-settings.tsx b/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/start-coords-settings.tsx
index d4a6e57c81b..b214dffcab5 100644
--- a/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/start-coords-settings.tsx
+++ b/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/start-coords-settings.tsx
@@ -25,6 +25,7 @@ import StartCoordsAngle from "./start-coords-angle";
 import StartCoordsCircle from "./start-coords-circle";
 import StartCoordsExponential from "./start-coords-exponential";
 import StartCoordsLine from "./start-coords-line";
+import StartCoordsLogarithm from "./start-coords-logarithm";
 import StartCoordsMultiline from "./start-coords-multiline";
 import StartCoordsPoint from "./start-coords-point";
 import StartCoordsQuadratic from "./start-coords-quadratic";
@@ -124,6 +125,21 @@ const StartCoordsSettingsInner = (props: Props) => {
                 />
             );
         }
+        case "logarithm": {
+            const defaultLogarithmCoords = getDefaultGraphStartCoords(
+                props,
+                range,
+                step,
+            ) as {coords: [Coord, Coord]; asymptote: number};
+            const currentLogarithmCoords =
+                props.startCoords ?? defaultLogarithmCoords;
+            return (
+                <StartCoordsLogarithm
+                    startCoords={currentLogarithmCoords}
+                    onChange={onChange}
+                />
+            );
+        }
         case "tangent":
             const tangentCoords = getTangentCoords(props, range, step);
             return (
diff --git a/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/types.ts b/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/types.ts
index 144613b0c59..4b933f3aaac 100644
--- a/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/types.ts
+++ b/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/types.ts
@@ -13,6 +13,7 @@ type GraphTypesThatHaveStartCoords =
     | {type: "segment"}
     | {type: "sinusoid"}
     | {type: "exponential"}
+    | {type: "logarithm"}
     | {type: "tangent"};
 
 export type StartCoords = Extract<
diff --git a/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/util.ts b/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/util.ts
index 0b9bfec005e..c546efbd245 100644
--- a/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/util.ts
+++ b/packages/perseus-editor/src/widgets/interactive-graph-editor/start-coords/util.ts
@@ -4,6 +4,7 @@ import {
     getAngleCoords,
     getCircleCoords,
     getExponentialCoords,
+    getLogarithmCoords,
     getLineCoords,
     getLinearSystemCoords,
     getPointCoords,
@@ -111,8 +112,14 @@ export function getDefaultGraphStartCoords(
                 range,
                 step,
             });
-        case "logarithm":
-            return undefined;
+        case "logarithm": {
+            const {coords, asymptote} = getLogarithmCoords(
+                {...graph, startCoords: undefined},
+                range,
+                step,
+            );
+            return {coords, asymptote};
+        }
         default:
             return undefined;
     }
@@ -202,6 +209,49 @@ export const getQuadraticEquation = (startCoords: [Coord, Coord, Coord]) => {
     );
 };
 
+export const getLogarithmEquation = (
+    coords: [Coord, Coord],
+    asymptote: number,
+) => {
+    const p1 = coords[0];
+    const p2 = coords[1];
+
+    // Guard: same y, point on asymptote, or points on opposite sides
+    if (p1[1] === p2[1]) {
+        return "undefined (points share the same y)";
+    }
+    if (p1[0] === asymptote || p2[0] === asymptote) {
+        return "undefined (point on asymptote)";
+    }
+
+    const ratio = (p1[0] - asymptote) / (p2[0] - asymptote);
+    if (ratio <= 0) {
+        return "undefined (points on opposite sides of asymptote)";
+    }
+
+    // Inverse exponential approach (mirrors getLogarithmCoefficients in kmath)
+    const bExp = Math.log(ratio) / (p1[1] - p2[1]);
+    const aExp = (p1[0] - asymptote) / Math.exp(bExp * p1[1]);
+
+    if (!isFinite(bExp) || !isFinite(aExp) || aExp === 0 || bExp === 0) {
+        return "undefined (invalid coefficients)";
+    }
+
+    const a = 1 / bExp;
+    const b = 1 / aExp;
+    const c = -asymptote / aExp;
+
+    return (
+        "y = " +
+        a.toFixed(3) +
+        "ln(" +
+        b.toFixed(3) +
+        "x + " +
+        c.toFixed(3) +
+        ")"
+    );
+};
+
 export const getAngleEquation = (
     startCoords: [Coord, Coord, Coord],
     allowReflexAngles: boolean = false,
@@ -249,9 +299,8 @@ export const shouldShowStartCoordsUI = (
         case "segment":
         case "sinusoid":
         case "absolute-value":
-            return true;
         case "logarithm":
-            return false;
+            return true;
         default:
             throw new UnreachableCaseError(graph);
     }