Log problem plus how to solve Big-omega & Big-O ?

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Dear vbforum

I'm having trouble doing these question please help, I have try to do it, but I don’t know is right or not. Please any smart people out there, show me the step to do it.

Thank You!

----------------------Question
Q1)Algorithm A uses 50n log n operations, algorithm B uses n^2 operations.
Determine the value of n such that A this better than B for N >= n .
Log(n) is base10 for A.
 
Q2)Suppose we are comparing implementations of insertion sort and merge sort on the same machine.
For inputs of size n, insertion sort runs in 8(n^2), while merge sort runs in 64n lg n steps. 
For which values of n does insertion sort beat merge sort?
 
Q3)What is the smallest value of n such that an algorithm whose running time is 100 n2 runs faster than
an algorithm whose running time is 2n on the same machine?
 
Q4)
2. Prove that f(x) = 10 + 100lg(x-3) is Big-omega
3. Prove that f(x) = 10 + 100lg(x-3) is Big-O
 
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----------------------Answer
I don’t ready know what do it mean by A beat B, I hope I get the arrow right.
Q1) 
A                B
50nlog(n) <= n^2
 
50nlog(n) <= n^2
----------  ----
n             n
 
50log(n) <= n
 
n=1 try it out
50log(1) <= 1
0 <= 1
0<=n<=1
 
 
 
 
Q2)
8n^2 >= 64nlgn
 
8n^2 >= 64nlgn
------  --------
n          n
 
8n >= 64lgn
 
8n >= 64lgn
----   --------
8         8
 
n >= 8lgn
 
n >= lg(n^8)
 
2^n >= n^8
 
Try to guess
 
n = 0
2^0 >= 0^8
1 >= 0 Yes
 
n=1
2^1 >= 1^8
2 >= 1 Yes
 
n=2
2^2 >=2^8
4 >= 256 No
 
I think 0 <= n <= 1
 
 
 
Q3)
100n^2 <= 2^n
 
Don’t know what to do, try to guess
n = 1/10
100(1/10)^2 <= 2^(1/10)
100(1/100)^2 <= 2^(1/10)
1 <= 2^(1/10)
1 <= 1.07
0 <= n <= 1/10
 
Q4) No Idea, can some one please show step for Big-omega & Big-O?
 
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Please help.