How to solve for x when x is an exponent on both sides

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    Solving Exponential Equations With Different Bases

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    The following diagram shows the steps to solve exponential equations with different bases.

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    How to solve exponential equations with different bases?

    Sometimes we are given exponential equations with different bases on the terms.

    In order to solve these equations we must know logarithms and how to use them with exponentiation. We can access variables within an exponent in exponential equations with different bases by using logarithms and the power rule of logarithms to get rid of the base and have just the exponent.

    How to solve exponential equations using logarithms?

    1. Isolate the exponential part of the equation.

      If there are two exponential parts put one on each side of the equation.

    2. Take the logarithm of each side of the equation.
    3. Solve for the variable.
    4. Check your solution graphically.

    Exam

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      solve for x in exponential