Simplifying an Expression using Logarithms

[jahaddow]

Ok, I have an Expression which is attached and it needs simplifying.
What I have done is got 12logx
But I don't think this is correct.
Another possible place I got to is logx⁴/logx^1/3
Which one is it?

 

[Dick]

Show your work, ok? One of those is correct and one isn't. The trouble is that the one that is correct isn't very 'simplified'.

 

[jahaddow]

Ok, so its obviously logx⁴/logx^1/3
The problem is, I am really stuck here, can't get any further!

 

[Dick]

Ok, so its obviously logx⁴/logx^1/3
The problem is, I am really stuck here, can't get any further!

Ok, that's the correct one. But now use log(x^b)=b*log(x). What do you get? log(x)/log(x) isn't log(x).

 

[jahaddow]

Ok so, 4logx/1/3logx
Would the answer be just 12?

 

[Dick]

Yes. Just 12.

 

[jahaddow]

Thankyou Very Much :D