LOGARITHMIC Equations
Properties of Logaritms
Exponential Equations
Exponential growth or decay?
EXPONENTS
100
Solve for x: x e =1
x=1
100
[3 6] + [2 5] [2 4] [4 7]
[5 11] [6 11]
100
Solve using substitution: 6x+3y=12 3x+y=5
(1,2)
100
Identify center and radius: 2 2 x + y =100
Center: 0,0 Radius: 10
100
2 3 x +x
5 x
200
Write in exponential form: log 81=4 3
4 3 =81
200
[1 0 -2] [-3 0 1] [4 1 6]-[2 5 -3] [2 -1 2] [-1 0 2]
[4 0 -3] [2 -4 9] [3 -3 0]
200
Solve using the elimination method: -3x+3y=3 3x+y=9
(2,3)
200
Identify center, vertices, and co vertices: 2 2 x +y -- -- = 1 16 25
Center: 0,0 Vertices: (5,0) (-5,0) Co-Vertices: (0,4) (0,-4)
200
4 5 x * x
20 x
300
Solve for x: log 3= 343 X
7
300
[8] [-2]x[-5 1 0] [4]
[17 5 -8]
300
Solve using either method: 5x+7y=-2 2x-7y=9
(1,-1)
300
Identify the center and the radius: 2 2 (x-3) +(y+7) = 144
Center:(3,-7) Radius: 12
300
2 3 9 +4
145
400
Expand the Logarithm: 3 log xy ___ 16
log x+ 3log y- log16
400
Find the inverse: [1 3 5] [0 3 5] [0 0 5]
[1 -1 0] [0 .3 -.3] [0 0 .2]
400
Solve using either method: 3x-8y=0 -2x=5y=-2
(16,6)
400
Write in standard form: 2 2 4x -9y =36
2 2 x y _ - __ 9 4
400
8 x __ 9 x
1 x
500
Condense the logarithm: log 4+log 5-log 2-log 6 3 3 3 3
log 5 3__ 3
500
Find the determinant: [3 0 1] [-3 4 2] [-2 1 -1]
-13
500
Solve using either method: 0.25x+0.5y=7.5 0.4x+0.5y=9
(10, 10)
500
Write in standard form: 2 2 9x +y =36 Is this a circle, ellipse or hyperbola?
2 2 x y -- + -- =1 4 36 Ellipse
500
5 --- 2 9
243
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