Using Properties of logarithms In Exercise, Use the properties of logarithms and a fact that In 2≈ 0.6931 and In 3 ≈1.0986 to approximate the logarithm. Then use a calculator to confirm your approximation.

(a) In 0.25

(b) In 24

(c) In (12) 1/3

(d) In 1/72

Step-by-step explanation:

Given that ln 2 = 0.6931 and ln 3 = 1.0986

We have to find the values for the given numbers

using properties of log

Properties of log are

log a+log b = log ab: log a-log b = log a/b

a) ln 0.25 = ln 1-ln 4 = - 2ln 2 = - 1.3862

b) ln 24 = ln 3 (2^3) = 3 ln 2 + ln 3 = 2.0793+1.0986

=3.1779

c) ln (12) ^ (1/3) = 1/3 ln (2^2*3) = 1/3 (1.3862+1.0986)

= 0.8283

d) ln (1/72) = - ln 72 = - ln 9 - ln 8

= - 3 ln 3 - 3ln 2

= - 5.2752