Logarithmic and exponential equations

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Presentation transcript:

Logarithmic and exponential equations Objectives: Solve Logarithmic Equations using the Properties of Logarithms Solve Exponential Equations

Logarithmic Equations 1. Express the equation in the form 2. Use the definition of a logarithm to rewrite the equation in exponential form 3. Solve for the variable 4. Check proposed solutions in the original equation. Include in the solution set only values for which

EX: Solve each equation. Exact answers 1. 2.

EX: Solve each equation. Exact answers 3. 4.

Logarithmic Equations 1. Express the equation in the form . This form involves a single logarithm whose coefficient is 1 on each side of the equation 2. Use the one-to-one property to rewrite the equation without logarithms 3. Solve for the variable 4. Check proposed solution in the original equation. Include in the solution set only values for which

EX: Solve each equation. Exact answers 5. 6.

Exponential Equations 1. Isolate the exponential expression 2. Take the natural logarithm or common logarithm on both sides of the equation 3. Simplify using one of the following properties 4. Solve for the variable

EX: Solve each equation. Exact answers 7. 8.

EX: Solve each equation. Exact answers 9 10

EX: Solve each equation. Exact answers 11.