San Diego State University Logarithmic Form College Algebra Exam 4

Exam 4Name: ________________________________
Show all your work for full credit: 100 points
Part 1: 65 points (in class)
Part 2: 35 points (take home)
Part 1:
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Q1. (9 points) A) Write the equation 64−1/2 = 8 in logarithmic form.
B) Use the change of Base Formula to evaluate 𝑙𝑜𝑔2 6
C) Use the Laws of Logarithms to expand the expression.
4𝑥 2
log (
𝑦3
)
Q2. (8 points) Solve the equation. Find the exact solution and rounded to two decimal places.
31−𝑥 = 52𝑥
1
Exam 4
Name: ________________________________
Show all your work for full credit: 100 points
Q3. (8 points) Solve the equation. Find the exact solution.
𝑙𝑜𝑔2 (𝑥 − 7) + 𝑙𝑜𝑔2 𝑥 = 3
Q4. (8 points) Suppose that $8,000 is invested in a saving account paying 5% interest per year.
How long will it take for the amount in the account to grow to $16,000 if interest is compounded
quarterly?
2
Exam 4
Name: ________________________________
Show all your work for full credit: 100 points
Q5. (10 points) a) Sketch the graph of the function. State its domain, range in the interval
notation. State its asymptote. Show the 𝑥 − and 𝑦 −intercepts on the graph.
𝑓(𝑥) = 3𝑥 + 2
3
Exam 4
Name: ________________________________
Show all your work for full credit: 100 points
Q6. (10 points) Radium—221 has a half-life of 30s. Suppose we have a 300 g sample.
a) Find a formula for the mass remaining after t seconds.
b) How much of the sample remains after 200 seconds?
c) After how long will only 20 g remain?
4
Exam 4
Name: ________________________________
Show all your work for full credit: 100 points
Q7. (12 points)
a)
b)
c)
d)
e)
Sketch the graph of the function.
State its domain, range in the interval notation
State its asymptote. Show the 𝑥 − and 𝑦 −intercepts on the graph.
Graph 𝑓 −1 (𝑥) on the same graph as part (a)
Find 𝑓 −1 (𝑥)
𝑓(𝑥) = 𝑙𝑜𝑔2 (𝑥 + 4) + 2
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