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Logarithms

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12

Logarithms

What are logarithms? Who was 'John - the man - Napier'?
Converting between log equations and index equations

 

Class notes, Blank notes

Ex8.06, Ex9.01

Theta pg 34 & 35

NuLake EAS Q173 - 194

13

Log Rules

Comparing the log rules to index manipulations
Simplifying Log expressions using the three log rules
Log(A) + Log(B) = Log(AB)
Log(A) - Log(B) = Log(A/B)
nLog(A) = Log(A)n

 

Class notes, Blank notes

Ex9.02

Theta pg 36 & 37

NuLake EAS Q195 - 218

14


Index Equations

Solving index equations using logs eg. 3x = 17

Activity
Index equations practice (www.transum.org)

Class notes, Blank notes

Ex9.03, Ex9.04

Theta pg 38 & 39 & 40

NuLake EAS Q219 - 233

 

Jump down to... Introduction | log & index form | Log rules | Index Equations

Log Introduction

Log264=6

"What is the power on 2 which gives 64?
The power is 6


Common logs are Log10  (base 10)
Natural Logs are Loge (base e = 2.71828...)
 

Index form
bp=q

Logs 'get at' the powers

 Log form
logb(q)=p

"log of q to the base b is p"
or
"Log base b of q is p"

 

 

Converting between log & index forms

1) First example

Solution

2) 2nd example

Solution

3) 3rd example

Solution

Mouse over key words

 

Summary:

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Log Rules

Three key log rules help to simplify & solve equations

Multiplying algebra terms means ADD the powers.

1) When we multiply numbers we ADD the logs.

 
 
Dividing algebra terms means SUBTRACT the powers.

2) When we divide numbers we Subtract the logs.

 
 
A power on a power means we MULTIPLY the powers.

3) When we raise a numbers by a power we MULTIPLY the log by that power.

 

 

Summary:

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Index Equations

1) Take the Logs of both sides

2) Use 3rd Log rule

3) Solve

Mouse over key words

 

Summary:

 

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Continue to Solving Equations