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

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11

step-by-step explanation:

32.50-7.50=25

225/25=11