We will use the following logarithm rules:
ln(a) + ln(b) = ln(ab)
ln(a) - ln(b) = ln(a /b)
aln(b) = ln(b)ᵃ
a) 4ln(2) + 2ln(3)
= ln(2)⁴ + ln(3)²
= ln (16 x 9)
= ln (144)
= 2ln (12)
b) 0.5ln(9) - ln(2)
= ln(√9) - ln(2)
= ln(3) - ln(2)
= ln (3 / 2)
c) 2ln(5) - 1
= ln(5)² - ln(e)
= ln (25 / e)
d) 0.25ln(81)
= ln(81)⁰.²⁵
= ln (3)
