Question

ln 2 + ln 8 - ln 4

ln 4

ln 6

ln 64

Answer 1

Use log rules: ln a + ln b = ln(ab) and ln a − ln b = ln(a/b).

- ln 2 + ln 8 − ln 4 = ln(2·8/4) = ln 4.
- ln 4 = 2 ln 2 ≈ 1.3862943611
- ln 6 ≈ 1.7917594692
- ln 64 = ln(2^6) = 6 ln 2 ≈ 4.1588830834

So the first expression equals ln 4; numerically ln 4 < ln 6 < ln 64.