The relationship isn't exact because the V BE voltages of Q 1 and Q 2 vary slightly as you adjust the potentiometer, but, in practice, this nonlinear—if not logarithmic—characteristic works well.

This article was originally published with the title “ A Natural Log: Our Innate Sense of Numbers is Logarithmic, Not Linear ” in SA Mind Vol. 19 No. 4 (August 2008), p. 13 doi:10.1038 ...