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Math Help - napierian logarithm problem

  1. #1
    Senior Member furor celtica's Avatar
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    napierian logarithm problem

    the function f is defined for positive real values of x by f(x)=12lnx - x^(3/2)
    the curve crosses the x-axis at points A and B
    a. by calculation, show that the value of x at point A lies between 1.1 and 1.2
    b. the value of x at the point B lies in the interval (n, n+1) where n is an integer. find n

    for a. i took 12lnx = x^(3/2) and turned it all around, getting e^x^(3/2) = x^12 etc. but i still have no idea of how to get the interval for x
    for b. i have no idea
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  2. #2
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    Quote Originally Posted by furor celtica View Post
    the function f is defined for positive real values of x by f(x)=12lnx - x^(3/2)
    This is f(x)= 12 ln(x)- x^{3/2}, not f(x)= 12 ln(x- x^{3/2})?

    the curve crosses the x-axis at points A and B
    a. by calculation, show that the value of x at point A lies between 1.1 and 1.2
    b. the value of x at the point B lies in the interval (n, n+1) where n is an integer. find n

    for a. i took 12lnx = x^(3/2) and turned it all around, getting e^x^(3/2) = x^12 etc. but i still have no idea of how to get the interval for x
    for b. i have no idea
    What is f(1.1)? What is f(1.2)? Are they of different sign? What does that tell you?

    For (b), Calculate f(n) for n= 2, 3, 4, 5,etc. until you find a root!
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  3. #3
    Senior Member furor celtica's Avatar
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    can ou please show me how to work through a.? is there another way of getting b.?
    its (12lnx) - (x^(3/2))
    what does 'are they of different sign' supposed to mean? i wouldnt be posting this if it was so simple for me, ive thought over it ok?
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