Fall 2009 Math 151
2
1.
Week in Review IX
ourtesy: David J. Manuel
(overing 4.3, 4.4)
1
1.
2.
2.
Rewrite log4 16 = 2 as an exponential
equation
3.
Calulate the following:
(b)
()
1
8
log9 27
log2
5 log 2 + 2 log 5 − log 8
2
3
3.
Solve for a: log8 a = .
4.
Use properties
of logarithms to rewrite
√
y2 z
logb
in terms of logb x, logb y, and
x
logb z .
5.
Solve for x: log(2 − x) + log(5 − x) = 1.
6.
Find the inverse of f (x) = e1/x
7.
Compute lim ln(e2x + 2ex ) − ln(2e2x + ex ).
8.
Compute and simplify the derivatives
of the following:
(a)
f (x) = (ln(−x))
(b)
y = (ln | sin x|)
()
Setion 4.3
(a)
Setion 4.4
x→∞
The formula to ompute the amount of
money A in an aount earning 100r%
interest ompounded mtimes per
year
r mt
after t years is A = P 1 +
. If
m
$10,000 in kept in a CD earning 3%
per year ompounded monthly, when
will the aount have $12,000?
1
g(x) = log3 (x2 + 4)
(d)
f (x) = x2 ln(2 + 3x)
(e)
x2 sin3 x
f (x) = √
1 + 2x
Use logarithmi dierentiation to nd
the derivative of y = ax
Find the derivative of f (x) = (1+x)1/x .