• Year 12

# Logarithmic and Exponential Functions

approx. 17 hrs

7 topics

43 concepts

Develop a deeper understanding of Logarithmic and Exponential Functions to enable you to approach your HSC examinations with confidence.

Available in
NSW

### Overview

Logarithmic and Exponential Functions is an essential component of Year 12 Mathematics Advanced as defined by the NSW Senior Mathematics syllabus.  We teach students how to apply mathematical techniques to solve fluency questions based on logarithmic and exponential equations. We help them connect ideas of calculus with algebraic, deductive and modelling skills to solve more complex problems.

### Topics & Concepts We Cover

This learning program is made up of the following 7 topics, broken down into 43 concepts.

• #### Solving Exponential Functions using Index Laws 3 concepts

1. Simplify algebraic expressions by applying index laws

2. Fractional indices

3. Solving exponential equations by equating the power

• #### Exponential and Logarithmic Form 3 concepts

1. Solve simple equations that involve logarithms

2. Converting exponential form to logarithmic form

3. Converting logarithmic form to exponential form

• #### Laws of Logarithms 7 concepts

1. Change of base formula

2. Log of a product

3. Log of a reciprocal

4. Log of 1

5. Log of a power

6. Log of a quotient

7. Log of a base

• #### Equations and Logarithms 4 concepts

1. Proving identities using the logarithmic laws

2. Solving equations involving the logarithmic function

3. Solving exponential equations by taking the logarithm of both sides.

4. Simplify expressions using the laws of logarithms

• #### Sketching Exponential and Logarithmic Functions 3 concepts

1. Sketching curves involving the exponential function

2. Sketching curves involving the logarithmic function

3. Examine the inverse relationship between logarithms and exponentials

• #### Calculus and the Logarithmic Function 11 concepts

1. Integrating functions in the form 1/(ax+b)

2. Finding the area of regions using techniques of integration involving the logarithmic function

3. Application of the derivative of the logarithmic function

4. Finding the volume of solids of revolution using techniques of integration involving the logarithmic function

5. Differentiate logarithmic functions involving the product rule

6. Differentiate logarithmic functions involving the quotient rule

7. Differentiate logarithmic functions involving the chain rule

8. Using the reverse chain rule to integrate functions in the form f'(x)/f(x)

9. Differentiate logarithmic functions with linear arguments

10. Product rule of differentiation

11. Quotient rule of differentiation

• #### Calculus and the Exponential Function 12 concepts

1. Differentiate exponential functions involving the chain rule

2. Integrating functions in the form e^(ax+b)

3. Application of the derivative of the exponential function

4. Differentiate exponential functions involving the quotient rule

5. Differentiate exponential functions involving the product rule

6. Finding the anti-derivative of an exponential function by considering a derivative

7. Integrating exponential functions with different bases

8. Differentiate exponential functions with different bases

9. Finding the volume of solids of revolution using techniques of integration involving the exponential function

10. Finding the area of regions using techniques of integration involving the exponential function

11. Differentiate exponential functions with linear arguments

12. Reverse chain rule

### What you'll get

Learning Content

• A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
• All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

• We match you to a private, expert tutor who is right for your needs and goals
• Our tutors are talented, tested, top ATAR achievers and subject experts
• During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Logarithmic and Exponential Functions

Reporting

• Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
• You and your parents receive a comprehensive feedback report after every session
• Every session is recorded and available for you to watch at any time, allowing you to review what was covered

### Ready to start this program?

Simply pick a time that works for you

We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

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