if 3^x=4^y=12^z then find the value of z ???
Umm... since you have not told us the values of x and y, we cannot determine the value of z.
But I'm guessing you want us to write the equation in the form z=?
$\displaystyle 3^x=4^y=12^z$
$\displaystyle log(3^x)=log(4^y)=log(12^z)$
$\displaystyle xlog(3)=ylog(4)=zlog(12)$
$\displaystyle z=\dfrac{xlog(3)}{log(12)}=\dfrac{ylog(4)}{log(12) }$
I doubt very much that this is the exact wording of the original question. You will only get an answer to the question you post, not the question you should have posted:
$\displaystyle 3^x = 12^z \Rightarrow \log_{12} 3^x = z \Rightarrow z = x \log_{12} (3)$. y is not even needed, although a similar answer in terms of y and no x can also be found.