Help with algebra problem involving logs

[strike2kill]

If (Log3 of x )( Logx of 2x)(Log2x of Y) =(log x of x^2) what is the value of Y?

http://www.wolframalpha.com/input/?i=(Log3+of+x+)(+Logx+of+2x)(Log2x+of+Y)+=(log+x+of+x^2)

Wolfram Alpha gives me that but i need to know how to get there. THANKS!

 

[strike2kill]

http://imgur.com/N8Ixn
just to be clear

 

[AlchemistK]

Do you know about the base changing theorem?

 

[I like Serena]

Welcome to PF, strike2kill!

If (Log3 of x )( Logx of 2x)(Log2x of Y) =(log x of x^2) what is the value of Y?

http://www.wolframalpha.com/input/?i=(Log3+of+x+)(+Logx+of+2x)(Log2x+of+Y)+=(log+x+of+x^2)

Wolfram Alpha gives me that but i need to know how to get there. THANKS!

What you would need is that ##\log_g a = {\log a \over \log g}##.
Can you find Y if you use this?


Btw, let's redo WolframAlpha with the proper expression:
http://www.wolframalpha.com/input/?i=log(3,+x)+*+log(x,++2x)+*+log(2x,+Y)+=+log(x,+x^2)
Actually Wolfram does not give the answer, although you can read it off the graph that it generates.

 

[strike2kill]

I'm sort of familiar with the change of base formula but I don't know how to apply it here

 

[I like Serena]

Replace (Log3 of x) by log(x)/log(3) and so on...

 

[HallsofIvy]

This has nothing to do with "Linear and Abstract Algebra" so I am moving it to "general mathematics".