# Stupid Equation

1. Dec 24, 2004

### Niels

How do I solve the following equation?

8n^2 = 64 n lg(n); (0 < n)

n = 8lg(n)
10^n = 10^8 n
...??? How do I isolate n?

2. Dec 24, 2004

### dextercioby

Who says u can???It's typically a transcendental equation.I suggest either graphical method (intersaction of graphs) (done by computer,maybe),or taking a calculator and "solving it through tries".Your equation may have 0,1 or maximum 2 solutions.

Daniel.

3. Dec 24, 2004

### Niels

I already did that with mathematica and got that one solution is x ~ 6.5... I just wanted to know if there was any algebraic solution...

I study running times of some algorithms and got this questions: for that values of n is the following inequality true:
8n^2 < 64 n lg(n)

Is there no analytical approach. This is a potential exam question and were not allowed to use calculators...

4. Dec 24, 2004

### matt grime

Is n supposed to be an integer?

5. Dec 24, 2004

### Niels

Yes, n is integer (input size for algorithm) but I'm interested in both cases. (real/integer)