- Mathematical Methods
- Year 12
Logarithmic and Exponential Functions
approx. 17 hrs
7 topics
43 concepts
Develop your skills in Logarithmic and Exponential Functions to approach your examinations with confidence.
approx. 17 hrs
7 topics
43 concepts
Develop your skills in Logarithmic and Exponential Functions to approach your examinations with confidence.
The Logarithmic and Exponential Functions program of learning covers the essential components of the Year 12 Mathematical Methods course and addresses learning outcomes from the Australian Curriculum. Students studying Year 12 Logarithmic and Exponential Functions apply mathematical techniques to solve fluency style questions based on logarithmic and exponential equations. They also connect ideas of calculus with algebraic, deductive and modelling skills to successfully solve more complex problems.
This learning program is made up of the following 7 topics, broken down into 43 concepts.
Fractional indices
Simplify algebraic expressions by applying index laws
Solving exponential equations by equating the power
Solve simple equations that involve logarithms
Converting logarithmic form to exponential form
Converting exponential form to logarithmic form
Change of base formula
Log of a power
Log of a product
Log of 1
Log of a quotient
Log of a base
Log of a reciprocal
Proving identities using the logarithmic laws
Solving equations involving the logarithmic function
Solving exponential equations by taking the logarithm of both sides.
Simplify expressions using the laws of logarithms
Sketching curves involving the exponential function
Sketching curves involving the logarithmic function
Examine the inverse relationship between logarithms and exponentials
Integrating functions in the form 1/(ax+b)
Differentiate logarithmic functions involving the chain rule
Finding the area of regions using techniques of integration involving the logarithmic function
Using the reverse chain rule to integrate functions in the form f'(x)/f(x)
Finding the volume of solids of revolution using techniques of integration involving the logarithmic function
Differentiate logarithmic functions involving the quotient rule
Application of the derivative of the logarithmic function
Differentiate logarithmic functions involving the product rule
Differentiate logarithmic functions with linear arguments
Product rule of differentiation
Quotient rule of differentiation
Differentiate exponential functions involving the product rule
Finding the area of regions using techniques of integration involving the exponential function
Integrating exponential functions with different bases
Finding the anti-derivative of an exponential function by considering a derivative
Differentiate exponential functions with different bases
Finding the volume of solids of revolution using techniques of integration involving the exponential function
Differentiate exponential functions involving the chain rule
Application of the derivative of the exponential function
Differentiate exponential functions involving the quotient rule
Integrating functions in the form e^(ax+b)
Differentiate exponential functions with linear arguments
Reverse chain rule
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