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

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

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