Solving for variable N when it is used as a base and exponent

  • Thread starter wjang
  • Start date
  • #1
1
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Homework Statement



I would like to solve the following equation for the variable "n"
The variable c represents any integer constant.

(n/2)^n = c

The goal is to get this in some form of n = ?

Homework Equations



The logarithm properties.

The Attempt at a Solution



I've tried using logs but I get stuck because there seems to be no way to somehow combine n as a base, and n as an exponent. Is this something that requires higher level math?

---------------------------------------
Let all logs be of base 2

(n/2)^2 = c
log(n/2)^n = log(c)
n*log(n/2) = log(c)
n(log(n)-log(2)) = log(c)
n(log(n)-1) = log(c)

Here I get stuck because any further logarithm manipulation only goes in circles.

Can anyone teach or point to me what kind of math I need to know to solve this please?
 

Answers and Replies

  • #2
53
0
Why didn't you move -log(2) over to the other side? Also, I like natural logs better when you're dealing with variables because you don't have to worry about the base.
 

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