Electrical – 12 potentiometers with multiplexer

Some rotary Pot's com in Linear, Audio and reverse Audio (where audio=log taper)

Actually it is "quasi"-log scale and not precision logarithm.

Notice it has a rapid transition from two different linear slopes. which gives you more sensitivity over a wider range of audio inputs rather than an apparent Off to ON effect if using a linear pot. If one adjusts audio equipment over a 30 dB range, that might occur in the 1st 5% of a Linear pot.

Such as

Many options may be selected when you order.

Precision Log pots would be mcuch more expensive than

As @Brian Drummond suggested, when you set the pins to input mode, they have high impedance, so they're not going to sink much current no matter how the external resistors are set up. The data sheet suggests using 10k or less because if you use a higher value than that, you'll need to increase the sample time of the ADC. The ADC works by allowing current from the input to charge a capacitor, then holding the the charge in the capacitor and using it as the input to a comparator. The ADC repeatedly generates candidate values and compares them with the capacitor charge until it finds the closest match; that value becomes the ADC output. If the impedance of the analog source is greater than 10k, the capacitor won't fully charge, and you'll get incorrect readings. You can increase the sample time, but that will decrease your sampling resolution (you'll get fewer samples per second). I don't think there's much reason to use a 100k pot over a 10k unless 100k is all you have.