Use the properties of logarithms, given that ln(2) ≈ 0.6931 and ln(3) ≈ 1.0986, to approximate the logarithm. use a calculator to confirm your approximations. (round your answers to four decimal places.) (a) ln(0.75) ≈ -0.5569 incorrect: your answer is incorrect. (b) ln(24) ≈ 8.3172 incorrect: your answer is incorrect. (c) ln( 3 18 ) ≈ 0.9635 correct: your answer is correct. (d) ln 1 72 ≈ 0.0458 incorrect: your answer is incorrect.

Since, logarithm properties are,

Given,

ln(2) ≈ 0.6931 and ln(3) ≈ 1.0986,

(a) ln(0.75) = ln(3/4)

= ln(3) - ln(4)

= ln(3) - ln(2²)

= ln(3) - 2ln (2)

= 1.0986 - 2(0.6931)

= -0.2876,

(b) ln(24) = ln(6 × 4)

= ln (6) + ln (4)

= ln (3 × 2) + ln(2²)

= ln (3) + ln(2) + 2 ln(2)

= ln 3 + 3 ln 2

= 1.0986 + 3(0.6931)

= 3.1779,

(c) ln (∛ 18)

≈ 0.9634

(d)

= -4.2765

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

from the figure we get,

the x axis shows   the months and,

the y-axis shows the number of satisfied customer.

each line or each cell in upward direction (y-axis) shows 500.

the appropriate scale for the y - axis is: -

a = 2000 customers

b = 4000 customers

c = 6000 customers

d = 8000 customers

e = 10000 customers

f = 12000 customers

g = 14000 customers