Pre-Calc
Chapter 3 Review Non-calculator Portion
Name___________________________________
1. Sketch the graph of the function. Identify the domain, range, and any
intercepts or asymptotes.
a. f ( x)  6 x 3
b. f ( x)  4 x
c. f ( x)  e x  2
c. f ( x)   log 2 x  3
d. f ( x)  log3 ( x  2)  3
e. f ( x)  ln x  2
2. Write in logarithmic form.
a. 43  64
b. 12 1 
1
12
3. Write in exponential form.
3
a. log16 8 
b. ln 6  1.79
4
4. Evaluate without a calculator.
a. log8 8.34
b. log 7 1
1
6
e. log9 9
f. log 36
i. ln e5  ln e 2
j. log 4 4
c. ln e
d. ln1
g. log 0.0001
h. 5log 2 8
k. log 4 2  log 4 32
l. 2 ln e8.5
5. Rewrite the expression in terms of ln 4 and ln 5 .
5
a. ln 20
b. ln 45  2ln3
c. ln
64
d. ln
6. Expand:
a. log 5 5x 2
b. log 7
5 y
x2
7. Condense:
a. log 2 5  log 2 x
1
c. ln 3  ln  4  x 2   ln x
3
b.
1
ln 2 x  1  2 ln x  1
2
c. ln[( x 2  1)( x  1)]
2
5
Calculator Portion
8. An initial deposit of $2,000 is made in an account compounding monthly at
8% annual interest. What is the amount in the account after 6 years?
9. An initial deposit of $1500 is made in an account compounding continuously.
The balance will triple in 40 years. What is the annual interest rate?
10. Evaluate log12 200
11. Solve for x algebraically. Round to 3 decimal places. Show work.
1
a. 8 x  512
b. 6 x 
c. log 7 x  4
216
d. e x  12
e. 3e 5 x  132
f. 4 x1  13  35
g. 4(5x )  68
h. e2 x  7e x  10  0
i. ln 3x  8.2
j. 3  2ln 4x  15
k. ln x  ln3  0
l. ln x  1  2
m. 4 log( x  6)  11
n. log  x 1  log  x  2  log  x  2 
12. Use a graphing calculator to find an approximate solution. ln x   x  5
13. The population of Anchorage Alaska is growing exponentially. In 1990 it was
264,000, in 2012 is was 315,000.
a. Let t = 0 correspond to 1990. Find an equation to represent the population of
Anchorage using the growth model y = aebt.
b. Find the population in 2025.
c. When will the population reach 400,000?
14. You invest $2050 into an account paying 0.25% interest compounded
continuously. How long will it take to double your money?
15. A house purchased in 1995 for $275000 is sold for $245,000 in 2008. Use
the model y = ae-bt to represent the depreciation of the house and then predict
the value of the house in 2020.
16. Find the exponential function y  y0 e kx that passes through the two points
(0,2) and (4,3).
17. The population of a city is P  2500e kt where t=0 represents the year 2000.
In 1945, the population was 1350. Find the value of k, and use this value to
estimate the population in the year 2010.