Lucan Community College Leaving Certificate Mathematics Higher Level

Lucan Community College Leaving Certificate Mathematics Higher Level Mr Duffy & Ms Mc. Kelvey More Laws of Logarithms © Ciarán Duffy

The Laws of Logs Log laws for Multiplying and Dividing We’ll develop the laws by writing an example with the numbers in index form.

The Laws of Logs A log is just an index, so to write this in index form we need the logs from the calculator. and So,

The Laws of Logs A log is just an index, so to write this in index form we need the logs from the calculator. and So,

The Laws of Logs A log is just an index, so to write this in index form we need the logs from the calculator. and So,

The Laws of Logs A log is just an index, so to write this in index form we need the logs from the calculator. and So, In general,

The Laws of Logs Any positive integer could be used as a base instead of 10, so we get: A similar rule holds for dividing. If the base is missed out, you should assume it could be any base e. g. might be base 10 or any other number.

The Laws of Logs SUMMARY Ø The Laws of Logarithms are: • 1. Multiplication law • 2. Division law • 3. Power law Ø The definition of a logarithm: leads to 4. 5. 6.

The Laws of Logs e. g. 1 Express the following in terms of (a) (b) (c) Solution: (a) ( Law 1 ) ( Law 3 ) (b) (c) Either ( Law 2 ) ( Law 4 ) Or ( Law 3 )

The Laws of Logs e. g. 2 Express in terms of and Solution: We can’t use the power to the front law directly! ( Why not? ) There is no bracket round the ab, so the square ONLY refers to the b. So, ( Law 1 ) ( Law 3 )

The Laws of Logs e. g. 3 Express each of the following as a single logarithm in its simplest form: (a) Solution: (a) (b) This could be simplified to (b)

The Laws of Logs Exercise 1. Express the following in terms of (a) Ans: (a) 2. Express (b) (c) in terms of and Ans: 3. Express the following as a single logarithm in its simplest form: (a) Ans: (a) (b)

The Laws of Logs

The Laws of Logs The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied. For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

The Laws of Logs SUMMARY Ø The Laws of Logarithms are: • 1. Multiplication law • 2. Division law • 3. Power law Ø The definition of a logarithm: leads to 4. 5. 6.

The Laws of Logs e. g. 1 Express the following in terms of (a) (b) (c) Solution: (a) ( Law 1 ) ( Law 3 ) (b) (c) Either ( Law 2 ) ( Law 4 ) Or ( Law 3 )

The Laws of Logs e. g. 2 Express in terms of and Solution: We can’t use the power to the front law directly! ( Why not? ) There is no bracket round the ab, so the square ONLY refers to the b. So, ( Law 1 ) ( Law 3 )

The Laws of Logs e. g. 3 Express each of the following as a single logarithm in its simplest form: (a) Solution: (a) (b) This could be simplified to (b)