Pre-Calculus 12 Notes

By: Gen L.

Lesson 5: Logarithmic / Exponential Equations

Types of Equations

There are three types of equations:

• Type I: All terms have logs.
• Type II: Some terms have logs.
• Type III: Exponentials w/o same base.

Type I Example

• State Restrictions:
  • Simplifies to

Type II Example

• State Restrictions:
  • Simplifies to

Type II Example, cont.

Type II Example 2

• State Restrictions:
  • Simplifies to

Type II, cont.

• No Solution. Oh well.

Type III Example

• Take log of both sides

Type III Example, cont.

Exponentials with Coefficients

• Be careful!
• Example:
• Wow! This is complicated.

Clearing the Static

• We have .
• With some shifting:

Calculation Flow

• Same Base (Type I)
  • Set values to each other
  • If logarithm, make sure answer fits restrictions.
• Dif. Base (Exponential, Type III)
  • Take log on both sides
  • Solve
• Dif. Base (Logarithmic, Type II)
  • Convert to Exponential
  • Solve, verify if answer fits restrictions (if needed).

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