Natural Log Scale by mbostock

index.html

<!DOCTYPE html>
<meta charset="utf-8">
<style>

.line {
  fill: none;
  stroke: steelblue;
  stroke-width: 1.5px;
}

.axis--x text {
  font: 10px sans-serif;
}

.axis--y text {
  font: oblique 15px Georgia, serif;
}

.axis path,
.axis line {
  fill: none;
  stroke: #000;
  shape-rendering: crispEdges;
}

</style>
<body>
<script src="//d3js.org/d3.v3.min.js"></script>
<script>

var superscript = "⁰¹²³⁴⁵⁶⁷⁸⁹",
    formatPower = function(d) { return (d + "").split("").map(function(c) { return superscript[c]; }).join(""); };

var margin = {top: 40.5, right: 40.5, bottom: 50.5, left: 60.5},
    width = 960 - margin.left - margin.right,
    height = 500 - margin.top - margin.bottom;

var x = d3.scale.linear()
    .domain([0, 100])
    .range([0, width]);

var y = d3.scale.log()
    .base(Math.E)
    .domain([Math.exp(0), Math.exp(9)])
    .range([height, 0]);

var xAxis = d3.svg.axis()
    .scale(x)
    .orient("bottom");

var yAxis = d3.svg.axis()
    .scale(y)
    .orient("left")
    .tickFormat(function(d) { return "e" + formatPower(Math.round(Math.log(d))); });

var line = d3.svg.line()
    .x(function(d) { return x(d[0]); })
    .y(function(d) { return y(d[1]); });

var svg = d3.select("body").append("svg")
    .attr("width", width + margin.left + margin.right)
    .attr("height", height + margin.top + margin.bottom)
  .append("g")
    .attr("transform", "translate(" + margin.left + "," + margin.top + ")");

svg.append("g")
    .attr("class", "axis axis--y")
    .attr("transform", "translate(-10,0)")
    .call(yAxis);

svg.append("g")
    .attr("class", "axis axis--x")
    .attr("transform", "translate(0," + (height + 10) + ")")
    .call(xAxis);

svg.append("path")
    .datum(d3.range(100).map(function(x) { return [x, x * x + x + 1]; }))
    .attr("class", "line")
    .attr("d", line);

</script>