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Math Help - xsin^-1 x

  1. #1
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    xsin^-1 x

    Hello :P

    How do i simplify this?:

    log4(16)*log4(4)

    And this:
    f(x)=xsin^(-1)x

    thanks...!
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  2. #2
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    Quote Originally Posted by MissWonder View Post
    Hello :P

    How do i simplify this?:

    log4(16)*log4(4)

    thanks...!
    Welcome to MHF!

    2 rules very handy for this type of problem are;
    log_{a}a=1
    log_{a}(b^c)=c \cdot log_{a}b


    So we know log_{4}4 = 1

    and we can simplify log_{4}16=log_{4}(4^2)=2log_{4}4.

    Therefore,

    (log_{4}16)(log_{4}4)

    =(log_{4}(4^2))(1)

    =(2 \cdot log_{4}4)(1)

    =(2)(1)(1)

    =2

    Does this help?
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  3. #3
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    Quote Originally Posted by MissWonder View Post

    f(x)=xsin^(-1)x
    you can't simplify this as written.
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  4. #4
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    Wee yes ;D I did not know the first part with "loga(A)=1".... Thanks kasper, you're the man!...

    What about "xsin^(-1)x"?
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  5. #5
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    x(sin^-1)x... better? I really don't know how to write it in a good way
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  6. #6
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    Quote Originally Posted by MissWonder View Post
    x(sin^-1)x... better? I really don't know how to write it in a good way
    Yeah, if you mean (x)sin^{-1}(x) as in (x)arcsin(x); I'm with Krizalid there.
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  7. #7
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    Yeah :P I really can't figure it out either! Maybe differentiate it is sufficient?..
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  8. #8
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    Quote Originally Posted by MissWonder View Post
    Yeah :P I really can't figure it out either! Maybe differentiate it is sufficient?..
    It's not so much that it can't be figured out, there is just no way to simplify that expression further.

    Keep in mind that differentiation and algebraic simplification are two very different things!

    Differentiating will bring out an entirely new function that is not at all equivalent to the original.
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  9. #9
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    I know.. But I can't simplify it.. So maybe differentiate it, and then simplify it?
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  10. #10
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    Quote Originally Posted by MissWonder View Post
    I know.. But I can't simplify it.. So maybe differentiate it, and then simplify it?
    No, no, because simplification is essentially rewriting a function such that it is equivalent to the original function and so it looks nicer and is easier to work with.

    If you differentiate, you lose that equivalency to the original function; so nothing to do with differentiation can be considered an algebraic simplification. Sure you *might* be able to simplify the derivative, but it would not be a simplification of (x)sin^{-1}(x).
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  11. #11
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    OMG! I just wrote an e-mail to my mathteacher.. She wrote that a differentiation is sufficient
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  12. #12
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    Quote Originally Posted by MissWonder View Post
    OMG! I just wrote an e-mail to my mathteacher.. She wrote that a differentiation is sufficient
    Perhaps your math teacher knew the exact instructions that came with the expression f(x)=x sin^(-1)x. Because we certainly didn't, despite several increasingly frustrated attempts to find out what they were.

    Next time post all the instructions given in the question.
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