Scavanger+Hunt+Answer+Key

=​ Answer Key =

Exponents
1. 2⁷=x Answer: 128
 * Question 1**

1. **"xxxxxxxx" equals x to the ? power. Answer: x to the 8th powe r
 * Question 2

1. What is 8 to the 4th power? ** Answer: 4096
 * Question 3

Question 1
1. 10 x = 10,000 Answer:


 * Rewrite this equation in logarithmic form: log 10 10,000 = x
 * Then, put it in a calculator and solve. The answer should be: 4 = x

Question 2
1. The Logarithm of x to the base 10 equals 0 1b. Does changing the base have any effect on 'x'? Why or Why not? Answer:
 * log 10 x = 0
 * Using the First Logarithmic Identity (log b 1 = 0), we know that x = 1.
 * Part (1b) No. Changing the base has no effect on the value of 'x' since any number raised to 0 will always result in 1 (x 0 = 1).

2. The Logarithm of x to the base 50 equals 1 Answer:
 * log 50 x = 1
 * Using the Second Logarithmic Identity (log b b = 1), we know that x = 50

Question 3
1. log 2 16 + log 2 4 Answer:
 * Using the Product Property, we get log 2 (16)(4)
 * Which is further simplified to log 2 64

2. log 5 8 - log 5 12 Answer:
 * Using the Quotient Property, we get log 5 (8/12 )
 * Which is further simplified to log 5 (2/3)

3. -log 3 4 + log 3 16 Answer:
 * This is a tricky one. Using the Quotient Property, we know that the '4' in -log 3 4 must be in the denominator because it is a negative logarithm (Not the same as the logarithm of a negative number). Therefore, the positive log 3 16 goes on the numerator, giving a result of log 3 (16/4)
 * Which is further simplified to log 3 4

4. log 10 100 9 Answer:
 * Using the Power Property, we get 9log 10 100

Real-World examples of Logarithms
Answer:
 * log 10 n = x, where 'x' is the number of minutes passed, and 'n' is the net number of cells that have accumulated. With how many cells did the experiment begin (Show this using the given equation)? How many cells have accumulated after 5min? 6min? 7min?
 * To figure out how many cells the experiment began with, we must go back before the experiment began, in other words, we make the time '0'. When we make x=0, the equation looks like this: log 10 n = 0. Using the First Logarithmic Identity (log b 1 = 0), we know that n = 1 . Therefore, the number of cells before the experiment began is 1.
 * After 5 min, we plug in 5 for x, and we get log 10 n = 5.
 * We then turn this into its exponential form, 10 5 = n
 * Resulting in 100,000 = n, In other words, 100,000 cells have accumulated after 5min since the experiment began.
 * The same concept is applied to 6min, and 7min, yielding 1,000,000 and 10,000,000 cells respectively.

Question 1

 * (A)
 * Bonus: (4 + 10x)0.5 = (4 ∙ 0.5) + (10x ∙ 0.5)

Question 2

 * 2t(3 + 8t) = (2t ∙ 3) + (2t ∙ 8t) = 6t + 16t 2

Question 3

 * -(4x - 3) = -4x + 3
 * 3(2y - 3) - 2y(8 +4y) = (3 ∙ 2y) + [3 ∙ (-3)] + [(-2y) ∙ 8] + [(-2y) ∙ 4y] = 6y - 9 -16y - 8 y 2 = -8y2 – 10y -9
 * -5t(t + 9) + 7(2t – t 2 ) = [(-5t) ∙ t] + [(-5t) ∙ 9] + (7 ∙ 2t) + [7 ∙ (-t 2 )] = -5t 2 -45t + 14t -7t 2 = -12t 2 - 31t


 * Polynomials

Question 1 Answer:** A coefficient is the numeric factor of your term.

Answer: When there are three terms it’s a trinomial.
 * Question 2**

Answer: Factorization is expressing a given expression or number as a product of its factors.
 * Question 3**

Complex or Imaginary Numbers
Answer:** Real numbers are all the positive numbers, negative numbers, and zero. Imaginary numbers are the square roots of -1, which are 'i' and '-i'.
 * Question 1

Answer:** The imaginary number 'i' cycles through 4 different values. i^1=i i^2=-1 i^3=-i i^4=1
 * Question 2

Answers:** a) 2//i// + 3//i// = (2 + 3)//i// = **5//i//** b) 16//i// – 5//i// = (16 – 5)//i// = **11//i//** c) (//i//)(2//i//)(–3//i//) = (2 · –3)(//i// · //i// · //i//) = (–6)(//i//2 · //i//) (–6)(–1 · //i//)(–6)(–//i//) = **6//i//**
 * Question 3