Starter Recall: In a previous lesson, we learned the “change of base” method for solving exponential equations. Try a few…Solve for x. (a) (b) (c)

Solutions (a) (b) (c)

Intro to Logarithms AS Maths with Liz Core 2

What happens if change of base method doesn’t work? E.g. Solve for x in the following In this case, there is no common base between 9 and 15. We could guess and check. However, to accurately solve problems like this, we need

Aims By the end of the lesson, you should be able to… convert between log and exponential form use the rules of logs to simplify expressions Previous Knowledge Rules of indices Solving exponential equations using change of base method

Log definition Logs provide us with a way to make the exponent the subject. For example… We know that To make the power the subject, we can rewrite it as

You try! Rewrite the following as logs. (a) (b) (c) (d)

You try! Rewrite the following as exponentials. (a) (b) (c) (d) (e)

Example 1 – Working out some logs without a calculator! Work out (a) (b)

Working out some logs without a calculator! You try… Work out (a) (b)

Logs in your calculator Work out (a) (b)

How to use your calculator to work out logs with bases other than In your calculator, MENU RUN MAT OPTN F4 CALC F6  F4 logab (3, 81) EXE

Using your calculator to work out logs. You try! Work out the following to two decimal places. (a) (b) (c)

Using your calculator to work out logs. You try! Rewrite the following as logs, then work out the value of x to two decimal places. (a) (b) (c)

Rules of Logs Logs have certain properties, just like indices. Over the next few slides, you will be given a series of logs to calculate. Be on the lookout for patterns and see if you can come up with the rules yourself! Work out: (a) (b) (c) Summarise your findings in your own words!

Rules of Logs Work out: (a) (b) (c) Summarise your findings in your own words!

Rules of Logs Work out: (a) (b) (c) Write a general rule in terms of a. Summarise your findings in your own words!

Rules of Logs Work out: (a) (b) (c) (d) (e) (f) (g) Summarise your findings in your own words!

Rules of Logs Work out: (a) (b) (c) (d) (e) (f) (g) Write a general rule in terms of a, m, and n. Summarise your findings in your own words!

Rules of Logs Work out: (a) (b) (c) (d) (g) Summarise your findings in your own words!

Rules of Logs Work out: (a) (b) (c) (d) (g) Summarise your findings in your own words!

Summary of Rules of Logs

Example 2 – Simplifying Logs Using the rules of logs, simplify the following expressions. (a) (b)

You try – Simplifying Logs Using the rules of logs, simplify the following expressions. Solution:

Example 3 – Simplifying Logs (Harder)

Exam Question – Jan. 2013

Mark Scheme

Independent Study Mymaths – Rules of LogsRules of Logs Worksheet – MEI “AQA Core 2 Algebra and Functions, Section 2: Exponentials and logarithms” (FOUND ON MY MOODLE PAGE) Due Tuesday, March 10 th Optional Practise Core 2 textbook:  Pg. 356, Exercise 7B  Pg. 360, Exercise 7C (#1 – 4)