Yes, the log(2) curve will grow “faster”. Its values are scaled by a constant factor, namely log2(10) = 3.32.

But when you render a chart for display, there’s an implicit scaling between the actual values and the position (in pixels) of that visual element (line).

This implicit scaling factor arbitrary, and chosen by the charting library, or manually by the chart author, to showcase the phenomena under investigation.

You could add to this chart another log line with base, say, 10 billion, and the other lines would be entirely squashed at the bottom. But the shape of each line would remain the same, preserving the change proportionality property.