- 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.
Simplify algebraic expressions by applying index laws
Fractional indices
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 reciprocal
Log of a power
Log of a base
Log of 1
Log of a quotient
Log of a product
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 logarithmic function
Sketching curves involving the exponential function
Examine the inverse relationship between logarithms and exponentials
Differentiate logarithmic functions involving the quotient rule
Finding the area of regions using techniques of integration involving the logarithmic function
Differentiate logarithmic functions involving the product rule
Differentiate logarithmic functions with linear arguments
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 volume of solids of revolution using techniques of integration involving the logarithmic function
Differentiate logarithmic functions involving the chain rule
Quotient rule of differentiation
Product rule of differentiation
Differentiate exponential functions involving the product rule
Finding the area of regions using techniques of integration involving the exponential function
Differentiate exponential functions involving the quotient rule
Finding the volume of solids of revolution using techniques of integration involving the exponential function
Application of the derivative of the exponential function
Finding the anti-derivative of an exponential function by considering a derivative
Integrating exponential functions with different bases
Differentiate exponential functions with linear arguments
Differentiate exponential functions with different bases
Integrating functions in the form e^(ax+b)
Differentiate exponential functions involving the chain rule
Reverse chain rule
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