Define the logarithmic integral li(x) as the integral of the function 1/(log t) from t = 2 to t = x, where x > 2 and "log" denotes the natural logarithm.
(a) Determine constants A and B such that li(x) can be expressed in the following two forms:
(i) li(x) = x/(log x) + A + g(x), where g(x) is the integral of the function
Please see the attached file for the fully formatted problems.
1. Convert the following equations into logarithmicform:
a. 9 = 4x
b. 3 = 6y
c. 5 = 7y
d. X = 9y
2. Convert the following equations into exponential form:
a. X = log3 6
b. -5 = log3 y
c. X = log4 y
d. 1000 = log5 Z
A. Convert to logarithmic equations. For example, the logarithmicform of "23 = 8" is "log2 8 = 3".
a) 16 3/2 = 64
b) ex = 5
B. Write the logarithmic equation in exponential form. For example, the exponential form of "log5 25 = 2" is "52 = 25".
a) log 3 27 = 3
b) log e 1 = 0
c) log 125 25 = 2/3
C. Use the
1.SOLVE A=1/2H(b1+b2) for b2
2. write 3-square root-36 in standard form Linear Functions
3.Find the slope of the line passing through the points (-2, 4) and (-3, 5).
a.1 b.-1 c.-9/5 d.-5/9
Zeros of Polynomial Functions
4.Find the zeros of P(x) = (
1. Do exponential functions only model phenomena that grow, or can they also model phenomena that decay? Explain what is different in the form of the function in each case.
2. A cell divides into two identical copies every 4 minutes. How many cells will exist after 3 hours?
Common and Natural Logarithms
1. For the exponential function ex and logarithmic function log x, graphically show the effect if x is doubled.
The exponential function f (x) = e^x
you will also need to graph f (x) = e^(2x).
The common logarithmic function f (x) = log x
You will also need to graph f (x) = log (2x).