SOLUTION: log(2)8, log(4)8, log(8)8, log(16)8, log(32)8, log(64)8, log(128)8 find an expression of the nth term of the sequence. write expression in p/q form. justify using technology.

Question 161686: log(2)8, log(4)8, log(8)8, log(16)8, log(32)8, log(64)8, log(128)8
find an expression of the nth term of the sequence. write expression in p/q form. justify using technology.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Find the nth term ():
,,,,,,,...
You can see that the base of the logarithms is always 2 to some power, and the power of 2 goes up like this, starting with the first term :,,,,,,,..., so for the nth term the base would be:
Now you can write the nth term as:
Now if you rewrite this in exponential form, you'll get:
Substitute to get:
Now since the bases (2) are equal, the exponents must be equal, so...
Divide both sides by n to get:
This is the expression for the nth term expressed in form.

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