Maths Internal Assesment                

        Logarithm Bases                                                          

LOGARITHM BASES

This internal assessment focuses on the logarithms. There are a few rules which govern all the concepts of logarithms:

=c, =b   where a>0, a≠1, b>0

=

  • Consider the following sequences. Write down the next two terms of each sequence.

log₂8, log₄8, log₈8, log₁₆8, log₃₂8, log₆₄8, log₁₂₈8

log₃81, log₉81, log₂₇81, log₈₁81, log₂₄₃81, log₇₂₉81

log₅25, log₂₅25, log₁₂₅25, log₆₂₅25, log₆₁₂₅25, log₁₅₆₂₅25

:
, , ,, ,


  • Find an expression for the nth term of each sequence. Write down your expression in the form  , where p, q . Justify your answers using technology.

=

Use the =  rule.

Then we apply the rule:  = a

We can cross  away on both sides.

What remains is:

We can do this for all the rows.

=

Use the =  rule.

Then we apply the rule:  = a

We can cross  away on both sides.

What remains is:

=

Use the =  rule.

Then we apply the rule:  = a

We can cross  away on both sides.

What remains is:  

4. Expressed in m, n and k.

Join now!

Use the =  rule and then we can change the base. We change the base to 10.

Then we apply the rule:  = a

We can cross  away on both sides.

What remains is: .  Derived from this we can conclude that the general expression for the nth term of each sequence in the form  thus is .

Examples to justify this statement using technology:

 =     ()

 =  = 1,5

 =

 =

  • Now calculate the following, giving your answer in the form , where p, ...

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