Question

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

Answer 1

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