Michigan State University - Diagnostic Exam

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5.10

  •   Solve the following equation for x. 2x x 2 - 10 ⋅ 2 + 16 = 0

    a) x = 1 b) x = 1 or 3 c) x = 2 log2-
       
    d) x = 3 e) x = 2 or 8

Solution:

x 2x x 2 w = 2 ⇒ 0 = 2 - 10 ⋅ 2 + 16 = w - 10w + 16 ⇒ 0 = (w - 2)(w - 8) ⇒ 2, 8 = w = 2x ⇒ x = 1, 3

Diagnostic:

If you miss this question please review the method of substitution.

Also, see 3.8: Exponential Equations and 2.3: Equations (Quadratic) .

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July 15, 2008