IB SL Math Portfolio- Logarithm Bases

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IB Math SL Portfolio Type 1

General Introduction:

In its simplest terms, a logarithm is an exponent. It is an exponent needed to produce a given number from a specific base. It is written in the form loggh=j, which denotes gh=j (g to the power of h equals j).

LOGARITHM BASES

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

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

log381, log981, log2781, log8181, ... log24381, log72981, ...

log525, log2525, log12525, log62525, ... log3,12525, log15,62525, ...

:

:

:

logmmk, logm^2mk, logm^3mk, logm^4mk, ... logm^5mk, logm^6mk , ...

Find an expression for the nth term of each sequence. Write your expressions in the form p/q, where p and q are integers. Justify your answers using technology.

The first sequence can be otherwise written:

log2^123, log2^223 , log2^323, log2^423, log2^523, ...

Here, I noticed a pattern: the base of each logarithm is 2n. Using this knowledge and the concepts of the change of base rule and verifying my theories with a GDC calculator,