Further explanations and examples

This page is aimed at anyone wanting to try logarithms, particularly students finishing the Scottish Higher Mathematics course (revised).
 
Applying the rules

Here are questions, using the logarithm rules shown on the other page:

1. Add the following logarithms together    (using rule 1)
    Example                log1020 + log1050
                              = log10(20 x 50)
                              = log101000
                              = 3

• log2128 + log21
• log39 + log381
• log432 + log48
• log5125 + log525
• log68 + log6162
• log77 + log749

                                           Worked Answers

2. Subtract the following logarithms     (using rule 2)
Example               log4 128 - log4 32
                           = log4 (¹²⁸/32)
                           = log4 4
                           = 1

• log2768 - log26
• log3162 - log32
• log4128 - log42
• log5500 - log5100
• log6648 - log63
• log107000 - log1070

                                        Worked Answers

3. Rearrange the following, simplifying answers into numbers where possible.    ( using rule three)
     Example            4log44                log216
                           = log44⁴             = log6³
                           = log4256          = 3log6     
                           = 4     

• 3log2
• 2log55
• 0.5log216
• log64
• log49
• log8

                                     Worked Answers
 

4. Now try these questions using all the rules above.
 Example               log42 - log48 + log416
                            = log4(²/8)x16
                            = log44
                            = 1

• log4 + log6 + log7
• log3 - log6 + log4
• log55 + 2log55

                         Worked Answers
 

               A brief history of John Napier               Rules of Logarithms
Answers to Examples                   Uses of Logarithms               Chemical uses of Logarithms
 
 
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