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Section 6.6 – Exponential & Logarithmic Equations

Learn how to solve exponential and logarithmic equations using methods such as rewriting as a logarithm or exponential, using the base-exponent property, substitution, and graphing.

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Section 6.6 – Exponential & Logarithmic Equations

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  1. Section 6.6 – Exponential & Logarithmic Equations

  2. Exponential & Logarithmic Equations Exponential equations are equations that contain variables in the exponent. Logarithmic equations are equations that contain variables in the argument of a logarithm.

  3. Exponential Equations • In order to solve exponential equations, we must get the variable out of the exponent. To do this, we can • if the equation contains one exponential, write it as a logarithm, • if the equation contains two exponentials, try to make the bases the same (Base-Exponent Property), • make each side of the equation the argument of a logarithm , or • use Substitution.

  4. Exponential EquationsBase-Exponent Property

  5. Exponential EquationsRewrite as a Logarithm Solve the exponential equation.

  6. Exponential EquationsRewrite as a Logarithm Solve the exponential equation.

  7. Exponential EquationsTake the log of both sides Since I can’t make the bases the same, make each side of the equation the argument of a logarithm.

  8. Exponential EquationsSolve by Graphing

  9. Exponential EquationsUse Substitution Since I have more than two terms, I can’t use either of the properties that we’ve used in the past. We will try to use substitution.

  10. Logarithmic Equations • In order to solve logarithmic equations, we must get the variable out of the logarithm. To do this, we can try to • combine the expression into a single logarithm, then write as an exponential, or • use the Logarithmic Equality Property. Recall that the domain of a logarithmic function is the set of positive real numbers. That means that once we have solved the equation, we must verify that the solution is in the domain. If the solution yields a logarithm of a negative number, we can’t use it!

  11. Logarithmic EquationsProperty of Logarithmic Equality

  12. Logarithmic EquationsWrite as an Exponential Is in the domain? Is in the domain?

  13. Logarithmic EquationsWrite as an Exponential Is in the domain? Is in the domain?

  14. Logarithmic EquationsProperty of Logarithmic Equality Is in the domain?

  15. Logarithmic EquationsSolve by Graphing

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