Question

Approximate: log5
4
7


–2.8760

–0.3477

0.7124

1.3738

Answer 1

Interpreting this as log base 5 of (4/7):

log_5(4/7) = ln(4/7) / ln 5
ln(4/7) = ln4 − ln7 ≈ 1.386294 − 1.945910 = −0.559616
ln5 ≈ 1.609438

So log_5(4/7) ≈ −0.559616 / 1.609438 ≈ −0.3477.

Answer: −0.3477.