Solving logrithmic functions

Lesson Title: Solving Exponential Equations

Objective:

By the end of this lesson, students will be able to:

• Solve exponential equations using the properties of exponents.

• Use logarithms to solve exponential equations when bases are different.

• Apply real-world problem-solving techniques involving exponential functions.

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Take 3 min to jot down.

The Problem

• Since the bases are the same, set the exponents equal:
  

Explanation:

Example 1:Solving Exponential Equations with the Same Base

Explanation

The Problem:

Example 2:Solving Exponential Equations with Different Bases Using Logarithms

Explantion:

The Problem:

Example 3:Solving Exponential Equations with e (Natural Exponential Functions)

Guided Practice (15 min):

Application &
Real-World Problem

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Solve: Show all steps mathematically.

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1. How llong will it take for the population to reach 8000?

2. Solve 8000-5000e^0.03t using logarithms.