Use the approximate logarithm values below to estimate the value of each of the following logarithms. indicate which properties you used.
log(12)

log(12) = 1.0791

Step-by-step explanation:

To solve:

log(12)

Now,

log(12) can also be written as :

⇒ log(4 × 3)

or

⇒ log(2 × 2 × 3)

or

⇒ log(2² × 3)

also,

we know the property of log function that

1) log(A × B) = log(A) + log(B)

2) log(Aᵇ) = b × log(A)

Thus applying the property (1) on the on the above rewritten form, we get

⇒ log(2² × 3) = log(2²) + log(3)

now applying the property 2, we get

⇒ 2 × log(2) + log(3)

also,

log(2) = 0.3010

log(3) = 0.4771

substituting the above values, we get

⇒ 2 × 0.3010 + 0.4771

or

⇒ 0.6020 + 0.4771

or

⇒ 1.0791

Hence,

log(12) = 1.0791

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

wholesale price is the initial price before markup. retail price comes after the markup.

a price of 8 bucks that's marked up by 100%   is

formula: initial price + (percent markup in fraction/decimal)(initial price)

8+(1)(8)

8+8

16

retail price is $16.