Pre-Calculus Workbook For Dummies, 3rd Edition
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Whether an exponential equation contains a variable on one or both sides, the type of equation you’re asked to solve determines the steps you take to solve it.

The basic type of exponential equation has a variable on only one side and can be written with the same base for each side. For example, if you’re asked to solve 4x – 2 = 64, you follow these steps:

  1. Rewrite both sides of the equation so that the bases match.

    You know that 64 = 43, so you can say 4x – 2 = 43.

  2. Drop the base on both sides and just look at the exponents.

    When the bases are equal, the exponents have to be equal. This step gives you the equation x – 2 = 3.

  3. Solve the equation.

    This example has the solution x = 5.

If you must solve an equation with variables on both sides, you have to do a little more work (sorry!). For example, to solve 2x – 5 = 8x – 3, follow these steps:
  1. Rewrite all exponential equations so that they have the same base.

    This step gives you 2x – 5 = (23)x – 3.

  2. Use the properties of exponents to simplify.

    A power to a power signifies that you multiply the exponents. Distributing the exponent inside the parentheses, you get 3(x – 3) = 3x – 9, so you have 2x – 5 = 23x – 9.

  3. Drop the base on both sides.

    The result is x – 5 = 3x – 9.

  4. Solve the equation.

    Subtract x from both sides to get –5 = 2x – 9. Add 9 to each side to get 4 = 2x. Lastly, divide both sides by 2 to get 2 = x.

About This Article

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About the book author:

Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of Trigonometry For Dummies and Finite Math For Dummies.

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