# Algebra II Honors Test – Logarithms

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PRECALCULUS HONORS
CHAPTER 3 REVIEW – EXPONENTIAL AND LOGARITHMIC FUNCTIONS
QUESTIONS #1-11 SHOULD BE COMPLETED WITHOUT THE USE OF ANY CALCULATOR!!!
1.
Find the solution to the equation ln (x2 + 3x )  ln 10 = 0 .
a) x = 5 or x = 2
b) x = 5 or x = 2
c) x = 5
d) x = 2
2.
Find the solution to the equation log x 8  1 .
3
a) x = 512
b) x = 24
c) x  1
d) x = 2
c) 3
d) 0
8
3.
Solve for x log 8  x  3 .
3
2
27
a) 6
4.
b) 3
The range for a logarithmic function is ______________?
a) all real numbers
5.
c) y &gt; 0
d) all rational numbers
Express as a single logarithm 5 log 3 x .
3
3
5
b) log 3 x
a) log3 x 5
6.
b) x &gt; 0
3
Solve for x log 2 (x + 7) + log 2 x = 3 .
a) x  7  3
b) 1
c) log3
3
x5
d) log 3
x5
3
c) not possible
d) none of these
c) not possible
d) none of these
c) 2
d) 4
x
x
7.
Evaluate log 1
3
1
.
3
a) x
b)
1
3
x
8.
What is the solution of  1   7 x 4 ?
7
 
a) 2
9.
b) 0
Find the approximate value of the expression log 16 160 .
a) 0.54
b) 1.83
c) 2.20
10. Find the value of the expression eln2.5 .
a) 30
b) 12.2
c) 2.5
d) 10
d) 0.9
11. Which of the following is not an exponential function.
a) f(x) = 5(2.7)x
b) f(x) = 7x2
c) f(n) = 125e0.12n
d) f(x) = 6.5  3 
 4
x
YOU MAY USE A CALCULATOR TO SOLVE QUESTIONS #1215. SHOW ALL WORK!!!
12. Janet deposited \$3200 at 4.5% annual interest, compounded quarterly. How long will it take this
money to triple in value?
13. Find the approximate solution(s) to the equation: 3(1.5) x + 10 = 280.
14. Find the solution(s) to the equation: 2 log a 3 + log a (x – 4) = log a (x + 8) .
15. The amount of pollutant, measured in parts per million, in Pine Lake can be modeled by the function
A(t) = 14e0.16t , where t is the number of years since a program began to clean up the lake. Approximately how long will it take
for the amount of pollutant in Pine Lake to reach 7 parts per million?
SKETCH THE FOLLOWING FUNCTIONS – NO CALCULATORS!!!
f ( x)  32 x  1
x 1
17. g ( x)  2  3
18. h( x)  2log 4 (3  x)  1
19. i ( x)   log 2 ( x  2)  4
16.
Be sure to review your homework problems, the worksheets on solving exponential and log equations. Know how to use the
change of base formula to simplify and evaluate log expressions without a calculator, and know your properties of logs and
exponents insideout.
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