Express the logarithm in terms of ln 2 and ln 7: ln(49/8)

Question

ln 2

ln 7

ln(49/8)

Answer 1

ln(49/8) = ln(7²/2³)

= ln(7²) - ln(2³) [Log Property used - ln(a/b) = ln(s) - ln(b)]

= 2*ln(7) - 3*ln(2) [Log Property used - ln(a^k) = k*ln(a)]

Properties Used

ln(a^k) = k*ln(a)

ln(a/b) = ln(s) - ln(b)