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Math Help - Couple questions involving continuity and logarithms....

  1. #1
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    Couple questions involving continuity and logarithms....

    #1. show that the given equation has at least one solution on the indicated interval.

    tanx=2x^2-1 on (-pi/4,0)

    I tried pluggin in -pi/4 and i got pi^2/8... now what?

    #2. Find a and b

    f(x) = tan(ax) if -pi/2<ax<0, -pi/2<bx<0

    4 if x=0

    ax+b if x>0

    ... i dont even know how to begin this one...

    #3. exp(log base e 25)

    i know that that is e^(log base e 25), but i dont know how to solve it after that...

    #4. log base2 (X^(log base2 X))=4

    so 16=x^(log base2 X)... but then what do i do?



    Thank You,
    Diggidy
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  2. #2
    Junior Member
    Joined
    Sep 2008
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    1. Plug in x = 0, what sign does it have?
    If f(x) is continuous, f(a) < 0 but f(b) > 0 then f(x) must cross the x-axis.

    2. Is f(x) continuous? If yes then f(x) as x->0 = f(0)

    3. Let m = exp(log base e 25)
    Take log of both sides on base e. What is m?

    4. log base2 (X^(log base2 X))=4
    X^(log base2 X) = 16
    If y = log base 2 X, what is X in terms of Y? Put that in the equation.
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