College Algebra Module 12 Exponential and Logarithmic Equations

College Algebra Module 12: Exponential and Logarithmic Equations and Models

Module Learning Outcomes: Exponential and Logarithmic Equations and Models • • • Introduction to Logarithmic Properties Introduction to Exponential and Logarithmic Equations Introduction to Exponential and Logarithmic Models

Logarithmic Properties

Learning Outcomes: Logarithmic Properties Introduction to Logarithmic Properties • Use the product rule for logarithms • Use the quotient rule for logarithms • Use the power rule for logarithms • Expand logarithmic expressions • Condense logarithmic expressions • Use the change-of-base formula for logarithms

Product Rule for Logarithms •

Quotient Rule for Logarithms •

Power Rule for Logarithms •

Expand Logarithmic Expressions Using the Logarithm Rules •

Condense Logarithmic Expressions Given a sum, difference, or product of logarithms with the same base, write an equivalent expression as a single logarithm: 1. Apply the power property first. Identify terms that are products of factors and a logarithm, and rewrite each as the logarithm of a power. 2. Next apply the product property. Rewrite sums of logarithms as the logarithm of a product. 3. Apply the quotient property last. Rewrite differences of logarithms as the logarithm of a quotient.

Change of Base for Logarithms •

Desmos Interactive: Change of Base Topic: change of base https: //www. desmos. com/calculator/umnz 24 xgl 1

Exponential and Logarithmic Equations

Learning Outcomes: Exponential and Logarithmic Equations Introduction to Exponential and Logarithmic Equations • Use like bases to solve exponential equations • Use logarithms to solve exponential equations • Use the definition of a logarithm to solve logarithmic equations • Use the one-to-one property of logarithms to solve logarithmic equations • Solve applied problems involving exponential and logarithmic equations

Exponential Equations •

Exponential Equations with a Common Base •

Exponential Equations with Unlike Bases •

Use Logarithms to Solve Exponential Equations •

Extraneous Solutions •

Logarithmic Equations •

Logarithmic Equations (cont. ) •

Exponential and Logarithmic Models

Learning Outcomes: Exponential and Logarithmic Models Introduction to Exponential and Logarithmic Models • Model exponential growth and decay • Use Newton’s Law of Cooling • Use logistic-growth models • Choose an appropriate model for data • Express an exponential model in base e

Exponential Growth •

Exponential Decay •

Desmos Interactive; Exponential Growth and Decay Topic: exponential growth and decay https: //www. desmos. com/calculator/4 zae 7 vnjfr

Quick Review •