Question

Write as a single logarithm.
ln(4) − 3ln(1/3) + ln(2)

Answer 1

ln(4) -3ln(1/3) + ln(2) = ln(216)

Explanation:

Hi there!

First, let´s write the expression:

ln(4) -3ln(1/3) + ln(2)

Apply the logarithm property: a ln(x) = ln(xᵃ)

ln(4) - ln(1/3³) + ln(2)

ln(4) - ln(1/27) + ln(2)

Apply the logarithm property: ln(a) - ln(b) = ln(a/b)

ln(4/(1/27)) + ln(2)

ln(108) + ln(2)

Apply the logarithm property: ln(a) + ln(b) = ln(a·b)

ln(108 · 2) = ln(216)

Have a nice day!