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Exponential & Logarithmic Functions
CHAPTER 4 Exponential & Logarithmic Functions
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Before we can talk about logs we need to do some review…
LAWS OF EXPONENTS
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Law #1 xmxn = xm+n Example: x2x3 x2x3 = x(2+3) = x5
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Law #2 xm/xn = xm-n Example: x4/x2 x4/x2 = x(4-2) = x2
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Law #3 (xm)n = xmn Example: (x3)4 (x3)4 = x(3x4) = x12
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Law #4 (xy)n = xnyn Example: (xy)3 (xy)3 = x3y3
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Law #5 xm/n = xn/yn Example: (x/y)3 (xy)3 = x3/y3
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Law #6 Example:
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Law #7 x-m = 1/xm Example: x-3 x-3 = 1/x3
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Solving Exponential Equation
An exponential equation is one in which a variable occurs in the exponent.
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Solving Exponential Equation
An equation in which each side can be expressed in terms of the same base can be solved using the property: bx = by Then x=y (and solve…)
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Example 1 5x = 53 So… x=3
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Example 2 101-x = 104 So… 1-x=4 1-4 = x -3 = x
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Example 3 2x = 32 2x = 25 x = 5 Express as a base 2!
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Example 4 32x-1 = 27 32x-1 = 33 2x-1 = 3 2x = 4 x = 2
Express as a base 3
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Example 5 (3x)2x+2 = 81 (3)2x2+2x = 34 2x2 + 2x = 4 2x2 + 2x – 4 = 0
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Example 6 4x+1 = 1/64 *note 64=43 So 1/64 = 4-3 4x+1 = 4-3 x + 1 = -3
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WORKSHEET side 1 (solve for x…)
HOMEWORK WORKSHEET side 1 (solve for x…) KEEP THIS SHEET!
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