APL, 7 bytes
⊃⍕⌊3×⍟2 Prints 2.
⊃⊃⍕⍕⌊⌊33××⍟⍟22 Prints 3.
Waaat?
Single:
3×⍟2 → 2.079441542 ⍝ 3 * ln 2 ⌊2.079441542 → 2 ⍝ floor ⊃⍕ → '2' ⍝ format and take first character Double:
⍟⍟22 → 1.128508398 ⍝ ln ln 22 ×1.128508398 → 1 ⍝ signum 33×1 → 33 ⍝ 33 * 1 ⌊⌊33 → 33 ⍝ floor ⊃⊃⍕⍕ → '3' ⍝ format and take first character