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Solve Exponential Equations

How to solve exponential equations

Before you try to solve exponential equations, you must be quite comfortable using the rules and laws of exponents. An exponential equation is simply an equation in which a variable appears in the exponent.

    Examples of exponential equations

  • 2x = 4
  • 22x = 16
  • 2x + 1 = 256

Steps to solve exponential equations



There are many different kinds of exponential equations. First, let's focus on exponential equations that have a single term on both sides. These equations can be classified into two different types.
  • Type #1) When the bases are of both terms are the same
  • Type #2) When the bases are of the terms are different
  • Solving Exponential Equations of the same base (type #1)
    Example: 4x+1 = 49
    Step 1)Ignore the bases, and simply set the exponents equal to each other 1) X+ 1 = 9
    Step 2) Solve for the variable 2) X = 9 − 1
      X = 8
    Solving Exponential Equations of with unlike bases (type #2)
    Example Equation: 43 =2x
    1) Rewrite the bases as powers of a common base (Ignore the exponents and Answer the following question: "4 and 2 are powers of what number? " Once you have your answer, rewrite both of the bases as powers of that number) 1) They are both powers of 2
    4 = 2²
    2) Substitute the rewritten bases into original equation 2) 43 =2x
    (22)3 =2x
    3) Simplify exponents 3) 26 = 2x
    4) Solve like an exponential equation of like bases 4) 6 = x
    Example Problems: solving exponential equations

    Demonstration Problem 2: Solving Exponential Equations

    Exponential Equations with Negative Exponents


    It is possible to use the steps outlined on this page to solve exponential equations with negative exponents. Again, it is necessary that both of the bases are powers of a common base. See the example below

    Mixed Practice problems
    Problem 1) Solve the following exponential Equation:
    9x = 81
    Answer
    Problem 2) Solve the exponential Equation below:
    Answer
    Problem 3) Solve the equation below:
    42x+1 = 65
    hint
    Problem 3) Solve this exponential equation:
    hint
    Problem 4) Solve this exponential equation:
    hint