- Mathematics Advanced
- 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.
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.
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.
This learning program is made up of the following 7 topics, broken down into 43 concepts.
Differentiate logarithmic functions with linear arguments
Differentiate logarithmic functions involving the chain rule
Differentiate logarithmic functions involving the product rule
Differentiate logarithmic functions involving the quotient rule
Application of the derivative of the logarithmic function
Integrating functions in the form 1/(ax+b)
Using the reverse chain rule to integrate functions in the form f'(x)/f(x)
Finding the area of regions using techniques of integration involving the logarithmic function
Finding the volume of solids of revolution using techniques of integration involving the logarithmic function
Product rule of differentiation
Quotient rule of differentiation
Differentiate exponential functions with linear arguments
Differentiate exponential functions involving the chain rule
Differentiate exponential functions involving the product rule
Differentiate exponential functions involving the quotient rule
Differentiate exponential functions with different bases
Application of the derivative of the exponential function
Integrating functions in the form e^(ax+b)
Finding the anti-derivative of an exponential function by considering a derivative
Finding the area of regions using techniques of integration involving the exponential function
Finding the volume of solids of revolution using techniques of integration involving the exponential function
Integrating exponential functions with different bases
Reverse chain rule
Sketching curves involving the exponential function
Sketching curves involving the logarithmic function
Draw and compare the graphs of the inverseÂ functionsÂ y=a^xÂ andÂ y=logax
Converting logarithmic form to exponential form
Converting exponential form to logarithmic form
Solve simple equations that involve logarithms
Change of base formula
Log of a product
Log of a quotient
Log of a power
Log of a reciprocal
Log of a base
Log of 1
Solving equations involving the logarithmic function
Proving identities using the logarithmic laws
Solving exponential equations by taking the logarithm of both sides.
Simplify expressions using the laws of logarithms
Fractional indices
Simplify algebraic expressions by applying index laws
Solving exponential equations by equating the power
Learning Content
An Expert Tutor
Reporting
Simply pick a time that works for you
Add your payment details securely online
We'll book in your first session and match you to an expert tutor
Starting at
per session
Fully flexible
PAYG and bundle plans
Use anytime
Access to practice questions