# napierian logarithm problem

• Sep 22nd 2009, 09:36 AM
furor celtica
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
• Sep 22nd 2009, 02:15 PM
HallsofIvy
Quote:

Originally Posted by furor celtica
the function f is defined for positive real values of x by f(x)=12lnx - x^(3/2)

This is \$\displaystyle f(x)= 12 ln(x)- x^{3/2}\$, not \$\displaystyle f(x)= 12 ln(x- x^{3/2})\$?

Quote:

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!
• Sep 22nd 2009, 10:05 PM
furor celtica
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?