Table of contents

0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

6. Exponential & Logarithmic Functions

Introduction to Exponential Functions

College Algebra

6. Exponential & Logarithmic Functions

Introduction to Exponential Functions

2:03 minutes

Problem 81

Textbook Question

Solve each equation. See Examples 4–6. 4^(x-2) = 2^(3x+3)

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Exponential Equations

Exponential equations involve variables in the exponent and can often be solved by rewriting them in a common base. Understanding how to manipulate exponents and apply properties of exponents is crucial for solving these types of equations.

Properties of Exponents

The properties of exponents, such as the product of powers, power of a power, and quotient of powers, allow us to simplify expressions involving exponents. For example, knowing that 4 can be expressed as 2^2 helps in rewriting the equation to a common base, facilitating easier solving.

Logarithms

Logarithms are the inverse operations of exponentiation and are useful for solving equations where the variable is in the exponent. Understanding how to apply logarithmic properties can help isolate the variable and find its value in exponential equations.