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I was doing algebra earlier today and I came across having to simplify [itex]log(x)\cdot log(x)[/itex]. Now obviously this can be described as an exponent, but im curious how to write it. Can I write it as [itex]log(x)\cdot log(x)={log^2}(x)[/itex] or should i do [itex]log(x)\cdot log(x)=(log(x))^2[/itex] I thought of this since if I did [itex]log(x)\cdot log(x)=log{(x)^2}[/itex] then that would mean that [itex]log(x)\cdot log(x)=2log(x)[/itex], which is not true. Same with other functions, like the sine function. How do I simplify [itex]sin(x)\cdot sin(x)[/itex]? Or even for any other function? [itex]f(x)\cdot f(x)={f^2}(x)?[/itex]

My second question about function notation is: does

[tex]f(x^2)=f{(x)^2}?[/tex]

ie: [itex]ln(x^2)=ln{(x)^2}?[/itex]

finally: my algebra teacher told me that you commonly write products with digits first, then constants, then variables (ie) [itex]2\cdot l\cdot \pi=2\pi l[/itex]. I have seen this order all over math books and sites. my question is, in what order do you write products with digits, constants, variables, AND functions?

finaly, should you try to put multipliers that have exponents at the end, for example [itex]\frac{2\cdot g}{\pi}=2g{\pi^{-1}}?[/itex]

Thank you.