Rewrite the expressions ln 5/64 and ln 2/5 in terms of ln 4 and ln 5.

Answer 1

This question is solved by applying the properties of logarithms, namely the quotient and exponent properties:

ln(a/b) = ln(a) - ln(b) and ln(a^b) = b*ln(a)

Use the quotient property to re-write original logarithm

----> ln(5/64) = ln(5) - ln(64)

We're not quite done because we're not in the terms asked for, ln(4) & ln(5), but...

64 = 4^3 ---> ln(64) = ln(4^3) and using the exponent property ln(4^3) = 3*ln(4)

Therefore

----> ln(5/64) = ln(5) - 3*ln(4)

This same process is used for the second part and I'll leave it to you Grace. Just remember, roots can be re-written as fractional powers, e.g. sqrt(4) = 4^(1/2)