Solving Exponential and Logarithmic Functions

Example (Solving Exponential and Logarithmic Equations)  Solve the exponential equation
    
    Solution. Since and so Therefore, and so and we have the solution of and by using the quadratic formula.  

Example (Solving Exponential and Logarithmic Equations) Solve the exponential equation

    Solve. We have and so Therefore, and so

Example (Solving Exponential and Logarithmic Equations) Solve the logarithmic equation .

    Solution. The idea is to combine the logarithms into one, as follows,
    




so that we can convert into exponential form, as follows,







We need to solve , and then check the denominator, we find After checking we find the solution is .

Example (Solving Exponential and Logarithmic Equations) Solve the exponential equation .

    Solution. We have,



Multiplying both sides by we have





Factoring we have



We only consider, because will lead to an extraneous solution of Therefore, the only solution is

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Solving Exponential And Logarithmic Equations
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/solving-exponential-and-logarithmic-equations.html