Logarithmic Functions
log381 = ?
4
Draw the basic shape of an exponential graph
Well done.
In matrices, what do you call the horizontal line and vertical line, respectively?
Rows & Columns
Variables in a system of equations don't share the same value.
True / False
Rewrite the equation in decomposed form:
12 / (x2 - 9)
2/(x-3) - 2/(x+3)
What property of logarithm is this?
logbmn = logbm + logbn
Product rule
Is this equation exponential growth or exponential decay?
f(x) = (1/2)x
Exponential decay
Determine the order of the matrix.
A = | 3 -1 0 6 |
| -2 7 1 4 |
2 x 4
For parallel equations, how many solutions are there?
zero
Rewrite the equation in decomposed form:
3x / (2x2 - x - 1)
1/(2x+1) + 1/(x-1)
What property of logarithm is this?
logb(m/n) = logbm - logbn
Quotient rule
The half-life of radium is about 1600 years. If 1 kg is present now, how much will be present after 3200 years?
0.25 kg
Find A - 2B
A = |2 -2|
|3 5|
B = |-3 10|
|12 8|
| 8 -22|
|-21 -11|
3x + 2y = 10
4x - 2y = 4
Find x and y.
x = 2
y = 2
Rewrite the equation in decomposed form:
(-5x + 4)/(x2 - x)
-4/x - 1/(x-1)
Solve for x:
log8(3x-4) = log8(5x+2)
x = -3
Which of the functions are equivalent?
I. f(x) = (2)3-x
II. g(x) = 8(2)-x
III. h(x) = 8/2x
I, II, and III
|1 2| |6 -2 8|
|5 -4| x |4 0 0|
|6 0| = ?
|14 -2 8|
|14 -10 40|
|36 -12 48|
3x + 2y = 6
x - y = -1
Find x and y.
(4/5 , 9/5)
(2x2 - 9x - 10)/(x2 - 5x)
2 + 2/x - 1/(x-5)
If log2 = x and log3 = y, express log24 in terms of x and y.
3x + y
A bacteria colony triples every 6 days. The population is P0 bacteria. What will the population P(t) be t days later?
P0(3)t/6
Use determinant to find the area of the triangle with the given vertices.
P(-2,-3), Q(3,2), R(-1,-8)
15 square units
6x - 2y + 3z = 6
2y - z = 8
z = 1
Find (x,y,z)
(2,9/2,1)
DOUBLE POINTS!!!
(15x2 - 11x - 5)/x(x + 1)(2x - 5)
1/x + 3/(x + 1) + 7/(2x - 5)