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Solving Logarithmic Equations

Example 1:. Solve the equation. Solving Logarithmic Equations. A logarithmic equation is an equation with an expression that contains the log of a variable expression. The following examples will show how to solve this type of equation. Method A.

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Solving Logarithmic Equations

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  1. Example 1: Solve the equation . Solving Logarithmic Equations • A logarithmic equation is an equation with an expression that contains the log of a variable expression. The following examples will show how to solve this type of equation. • Method A Exponentiate both sides of the equation, using base 2. In other words, write both side of the equation as exponents of base 2.

  2. Solving Logarithmic Equations Original problem Exponentiate Use inverse property to simplify … Evaluate the exponential …

  3. Solving Logarithmic Equations • Method B Original problem Use the definition of a log to express the equation in exponential form. Evaluate the exponential …

  4. Solving Logarithmic Equations • Example 2: Solve the following equation. Get the log expression on the left side by itself. Note that ln is a log with base e.

  5. Solving Logarithmic Equations Method A Method B

  6. Example 3: Solve the following equation (nearest hundredth). Solving Logarithmic Equations Use the Product property to combine the logs. Note that “log” is a log with base 10. Now either exponentiate (Method A) or use the definition of a log (Method B) to get …

  7. Solving Logarithmic Equations Use the quadratic formula to solve for x. Written as decimals (nearest hundredth), the solutions are ...

  8. The solution to the equation is Solving Logarithmic Equations • Go back and look at the original equation and compare with the answers. • Note that for the solution x = - 5.36, the expressions (x - 2) and (x + 4) will both be negative. Since the logarithm of a negative number is undefined, we must throw this extraneous solution out.

  9. Solving Logarithmic Equations • Example 4: Solve the following equation. Use the Quotient property to combine the logs on the left hand side of the equation. Equating the two expressions yields ...

  10. Solving Logarithmic Equations Solve for x.

  11. Solving Logarithmic Equations END OF PRESENTATION Click to rerun the slideshow.

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