Answer:
a)
a1 = log(1) = 0 (2⁰ = 1)
a2 = log(2) = 1 (2¹ = 2)
a3 = log(3) = ln(3)/ln(2) = 1.098/0.693 = 1.5849
a4 = log(4) = 2 (2² = 4)
a5 = log(5) = ln(5)/ln(2) = 1.610/0.693 = 2.322
a6 = log(6) = log(3*2) = log(3)+log(2) = 1.5849+1 = 2.5849 (here I use the property log(a*b) = log(a)+log(b)
a7 = log(7) = ln(7)/ln(2) = 1.9459/0.6932 = 2.807
a8 = log(8) = 3 (2³ = 8)
a9 = log(9) = log(3²) = 2*log(3) = 2*1.5849 = 3.1699 (I use the property log(a^k) = k*log(a) )
a10 = log(10) = log(2*5) = log(2)+log(5) = 1+ 2.322= 3.322
b) I can take the results of log n we previously computed above to calculate 2^log(n), however the idea of this exercise is to learn about the definition of log_2:
log(x) is the number L such that 2^L = x. Therefore 2^log(n) = n if we take the log in base 2. This means that
a1 = 1
a2 = 2
a3 = 3
a4 = 4
a5 = 5
a6 = 6
a7 = 7
a8 = 8
a9 = 9
a10 = 10
I hope this works for you!!
Answer:
x=25 or x=0
Step-by-step explanation:
4x(x−25)=0
Step 1: Simplify both sides of the equation.
4x2−100x=0
For this equation: a=4, b=-100, c=0
4x2+−100x+0=0
Step 2: Use quadratic formula with a=4, b=-100, c=0.
x=−b±√b2−4ac over 2a
x=−(−100)±√(−100)2−4(4)(0) over 2(4)
x=100±√10000 over 8
x=25 or x=0
Answer:
See below.
Step-by-step explanation:
t represents time (probably years).
The population of bobcats can't be negative, so negative values in the range do not make sense.
The function is continuous, but you're probably only looking at discrete values.
Answer: question 1: 20 question 2: 21 question 3: 17, 19, 23
Step-by-step explanation:
