Exploring Logarithms ⇒ Laws of Logarithms
1. a) Find the value of the following:
i) log​6​6
ii) log10
iii) log​x​ x
iv) ln​e
b) Write and verify the general rule for expressions in this form.
2. a) Find the value of the following:
i) log​7​1
ii) log1
iii) log​e​1
iv) log​x​1
b) Write and verify the general rule for expressions in this form.
3. a) Find the value of the following:
i) log​8​63 and log​8​7 + log​8​9
ii) log​12​24 and log​12​3 + log​12​8
b) Identify the possible general rule from above and write this down.
c) Verify that your general rule works.
4. a) Show that: log(20/5) = log20 − log5
b) Write ln30 as the difference of two logarithmic expressions.
c) Write and verify the general rule for expressions in this form.
5. a) Evaluate the following:
i) log14​3​ and 3log14
ii) log​7​20​5​ and 5log​7​20
b) Identify the general rule from above and write this down.
c) Verify that your general rule works.