# I am going to go through some logarithm bases, by continuing some sequences and finding an equation to find the nth terms in the sequences

by rbru9887 (student)

Logarithm Bases

In the next few examples I am going to go through some logarithm bases, by continuing some sequences and finding an equation to find the nth terms in the sequences in terms offor the first part.  Then for the second part, find an equation to figure out the third term in terms of from the given logarithms, after I will check my equation with several examples created by myself and check the validity of the equation, and the scope and limitations of a, b, and x.

PART 1:

With the four sequences given I will find the next two terms in each sequence then change the first three sequences into the form of the forth sequence which is necessary to find the equation to find the nth  term.  Finally for all four sequences I will check the validity by using my calculator and finding the 10th term and proving that my equation works.

1. Log28, log48, log88, log168, log328, log648, log1288
2. Log381, log981, log2781, lg8181, log24381, log72981
3. Log525, log2525, log12525, log52525, log312525, log1562525

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By changing the first three sequences to the form of the forth sequence it changes the subscripts.  Each subscript will have a raised power and that is the same as the number in the sequence it is or the nth terms.  By setting one of the logarithms in the sequence to y with a raised power of n subscript you can change the equation to exponential form and solve for y to find the equation for the nth term.

1. Log28, log48, log88, log168, log328, log648, log1288

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= y                (2n)y= 23    the 2’s will cancel out and give you  ny= 3               y=

Next to prove this I put

into my calculator. 10 as the nth term and that equals .3 I also put in the calculator to get .3 they equal the same which means the equation works.

1. Log381, log981, log2781, lg8181, log24381, log72981

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