Question

Simplify

a) 4ln2 + 2ln3
b) 0.5ln9 - ln2
c) 2ln5 - 1
d) 0.25ln81

Answer 1

d) 0.25ln81 is in simplest form

Answer 2

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)