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- Evaluate the following expressions. If this is not possible, state the reason. (3 pts. each)
a) ln e
5x
b)
2
log
c)
3
2 log 7
d)
6
log 3
e) log 3
(-9) f)
2
ln
x
e
- Expand the expression as a sum, difference, and/or constant multiple of logarithms. (4 pts.)
5 2
5
ln
x e
z
- Which, if any, of:
7
7 7 7
7
5 log 5
log , , log 5 log 2
2 log 2
, are equivalent? (3 pts.)
- Use the properties of logs to show that
3
2
log 10
and
3
2
log 20 are equivalent. (5 pts.)
- Prove, or disprove that f(x) = h(x) where f(x) = 16(
-2x
) and
2
x
h x
are equivalent. (6 pts.)
- Solve the following equations or indicate that no solution exists. (10 pts.)
a) log 3
(7-x) + log 3
(1-x) = 1 b)
2 1
x
- Radioactive Radium-226 has a half-life of about 1600 years. (6 pts.)
a) After 3000 years, what percentage of a sample remains?
b) How long would it be before only 70% of a sample remains?
- Let
2
f ( ) x x 3 x 5.
a) Use the difference quotient and limits to find
f ( ) x
. Show all steps.
b) Use your result to find the equation of the line tangent to f at x = 2. (10 pts.)
- Let
2
x x
f x
x x
; give the domain, range, intercepts, and asymptote(s) of f. Justify each response. Then
plot key points and sketch the graph. (Use limits to justify asymptotes.) (10 pts.)
- Graph 2
g x ( ) 3log ( x 2) (8 pts.)
- Find a formula for the fifth degree polynomial in the graph. (5 pts.)
