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Techniques for Solving Logarithmic and Exponential Equations

This guide provides effective strategies for solving logarithmic and exponential equations. Begin by isolating the logarithmic or exponential expression on one side of the equation. Aim to unify the bases, allowing for easier manipulation. When necessary, take the logarithm or natural logarithm of both sides, applying logarithmic properties to simplify and isolate the variable. Several examples demonstrate these techniques in action, including step-by-step solutions to various problems. Use a calculator to aid in finding the precise values for each solution.

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Techniques for Solving Logarithmic and Exponential Equations

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  1. Solving Equations

  2. To Solve Log and Exponential Equations • Get the exponential/logarithmic expression on one side by itself • Try to get both bases to be the same • Take the log or ln of both sides and apply the properties of logs to solve the equation • Use the calculator

  3. Ex. 1 Solving Exponential and Logarithmic Equations Problem Rewritten Solution a) b) c)

  4. Ex. 1 Solving Exponential and Logarithmic Equations Problem Rewritten Solution d) e) f)

  5. Ex. 2 Solve each Equation

  6. Ex. 3 Solve Divide both sides by 4 Take logarithm of both sides Inverse Property Solve for x (multiply both sides by ) Use a calculator

  7. Ex. 4 Solve Add 4 to both sides Divide both sides by 2 Take log (base 3) of each side Inverse property Add 5 to each side Divide both sides by 2 Use a calculator

  8. Ex. 6 Solving Logarithmic Equations To solve a logarithmic equation, you write it in exponential form.

  9. Ex. 7 Solve Subtract 5 from both sides Divide both sides by 2 Exponentiate each side. Inverse Property Use a calculator

  10. Ex. 8 Solve Divide both sides by 2 Exponentiate each side Inverse property Divide both sides by 3

  11. Classwork WORKBOOK PAGE 181 TOTD: 10, 20, 26 HOMEWORK PAGE 161: 2 – 35 MIDDLE COLUMN

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