(The green linked lessons can be clicked on to see the lesson and are included in the Basic Membership!)

### Composite Functions

- 2007 Q2 Find the composite function fog of two exponential functions.
- 2009 Q4 Find the correct composite function of a circular function and a log function.
- 2010 Q10 Find the composite function of an exponential and a log function.

### Domain and Range

- 2006 Q7 Find the maximal domain of a log function.
- 2007 Q14 Find the maximal domain of a log function.
- 2009 Q3 Find the maximal domain of a log function.
- 2012 Q5 Find the maximal domain and the range of a log function.
- 2013 Q5 Find the correct maximal domain and range of a log function.
- 2013 Q5 Find the maximal domain of the function f+g

### Finding Pronumerals

- 2000 Q9 Find the value of ‘a’ if x=4 is a solution to the log equation.
- 2001 Q10 Find the values of the pronumerals from the graph of the exponential function.

### Graphs

- 2003 Q4 Which graph is likely to be that of the exponential equation?
- 2005 Q5 Sketch the graph of the exponential function and find the rule of the inverse function.
- 2006 Q22 Which of the graphs could be the graph of the log function?

### Inverse Functions

- 2004 Q3 State the domain and range of the log function, find the rule of the inverse function.
- 2016 Q2 Find the rule and the domain of the inverse function of the exponential function.
- 2008 10 Find the rule and domain of the inverse function.
- 2016 Q5 Find the rule for h=fog, show that h= f((g(x))
^{2}), Find rule of the inverse function. - 2002 Q11 Which of the following functions is not a one to one function?
- 2006 Q6 The log function will have an inverse function for what value of ‘a’?
- 2009 Q16 Which function is the correct inverse function of the exponential function?

2013 Q3 Which graph is the graph of the inverse of the exponential function?

### Points of Intersection

### Simplifying Expressions

- 2000 Q10 Simplify the exponential expression.
- 2001 Q5 Find the equivalent log expression.
- 2002 Q10 The original expression can be simplified to which one of these expressions?
- 2011 Q22 The log expression can be simplified to which one of these?

The video below has my solution to Question 5 from the 2013 VCAA Maths Methods Short Answer exam. This type of question relies on an understanding of the log and index laws and which ones to use when solving log & exponential equations. You also need good algebra skills to get the correct answer – 54% of students answered part a correctly and 64% answered part b correctly.