Algebra 2
Exponentials & Logarithms Test
Name: ____________________________ Per _____
Date: _____________________
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x 5
1
1. Graph the function: y  6     2 . (Make the
3
parent graph dotted, and the final graph solid.
Label the asymptote.)
a. What is the Domain?
a. All Real numbers
b. All real numbers greater than 0
c. All real numbers greater than 2
d. All real numbers less than 5
b. What is the Range?
a. All Real numbers
b. All real numbers greater than 0
c. All real numbers greater than 2
d. All real numbers less than 5
c. What is the asymptote of the final graph?
a. y  2
b. x  2
c. x-axis
d. y-axis
2. Graph the function: y  log( x  3)  2 . (Make the
parent graph dotted, and the final graph solid.
Label the asymptote.)
a. What is the Domain?
a. All Real numbers
b. All real numbers greater than 0
c. All real numbers greater than -2
d. All real numbers greater than -3
b. What is the Range?
a. All Real numbers
b. All real numbers greater than 0
c. All real numbers greater than -2
d. All real numbers greater than -3
c. What is the asymptote of the final graph?
a. y  2
b. x  3
c. y  3
d. y  axis
Copyright © 2010 Sarah Marsh
3. Simplify each expression without using a calculator:
a. log 9 1 
b. log 3 27 x 
d. 10 log(x  4 ) 
c. e ln 0.5 
1
2
4. Expand the expression: ln 3 x =
5. Condense the expression: 4(log 6  log 2) 
6. Find the inverse of y  ln x .
x
5
7. Tell whether the function f ( x)    represents exponential growth or exponential decay.
4
EXPLAIN how you know.
8. Solve the equation. Check for extraneous solutions. (Leave all answers in log, base 10. Change bases
if necessary.)
a. 7 6 x  49 4 x 5
b. 5 x 1  3
c. e 4 x  1  9
Copyright © 2010 Sarah Marsh
d.
log 4 (4x  5)  log 4 ( x  10)
e. log( 5 x)  12  10
f.
log 4 ( x  12)  log 4 x  3
9. (Extra Credit) The value of a new car purchased for $24,900 decreases by 10% per year.
a. Write an exponential decay model for the value of the car.
b. After how many years will the car be worth half its purchase price?
Copyright © 2010 Sarah Marsh