I have the following function to prove that its time complexity is less or equal to O(xlogx)

**f(x) =xlogx+3logx2**

I need some help to solve this.

Answer:

Given,

```
f(x) = xlogx+3logx^2
= xlogx+6logx // since log (a^b) = b log a
```

As we know, ** f(x) = O(g(x)), if | f(x) | <= M. | g(x) |, where M is a positive real number**.

Therefore, for M>=7 and x varying in the real positive range,

```
M . x log x >= x log x + 6 log x
>= (x+6) log x.
f(x) = x log x + 3log x^2
= O(x log x).
```

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