Answer: In 3
SOLVINGS
What is 3 ln 3 - ln 9 expressed as a single natural logarithm
Since ln (m^n) = n⋅ln (m) … natural logarithmic property
We can further simplify the expression 3 ln 3
3 In 3 = In (3^3)
Therefore, 3 ln 3 - ln 9 = In (3^3) – In 9
Since ln(m/n) =ln(m) – ln(n) … natural logarithmic property
We can further simplify the expression In (3^3) – In 9
In (3^3) – In 9 = In [(3^3)/(9)]
= In (27/9)
= In 3
Therefore, 3 ln 3 - ln 9 expressed as a single natural logarithm is In 3.
To find the rate<span> of change, find the total change in price and then divide it by number of years over which it changed. So the answer is </span><span>$0.603</span><span> which is </span><span>$0.20 per pound per year</span><span>.</span>
Answer:
24 cm
Step-by-step explanation:
8+8=16
4+4=8
8+16=24 cm
*Perimeter includes adding all sides, area is multiplying all sides.
Okay, so you know that the perimeter of the pen is 28 feet. Now we need the separate side lengths.
P = 28 ft.
Length = x
Width = (1/2)x + 2
So now we can plug in the little equations of length and width into a perimeter formula:
2(x) + 2((1/2)x + 2) = 28
Distribute the 2's and solve as needed.
2x + x + 4 = 28
3x + 4 = 28
3x = 24
x = 8
To find the width, just plug in 8 for x in our little equation:
(1/2)(8) + 2
= 6
So, the length is 8 feet and the width is 6 feet.
