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

I need help understanding the forms and characteristics of exponential and logarithmic.
1. What are the general forms of function for exponential and logarithmic?
2. Please show a simple example of each exponential and logarithmic functions
3. What are at least four characteristics of graphical representation for each e

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

Let f(x) = (x^(3x) (4x-1)^8)/sqrt(8x^(2)+10)
If we use the method of logarithmic differentiation to find f '(x), we obtain f '(x) in the form
f ' (x)=[(x^(3x) (4x-1)^8)/sqrt (8x^(2)+10)] [(A(x) + (B(x)/4x-1) + (C(x)/8x^(2)+10)]
where A(x), B(x) and C(x) are functions of x. Find them.
A(x)=______
B(x)=______
C(x)=_

The problems below follow closely the examples shown in the background materials. Complete these problems showing your work and turn them in by the end of the Module.
1. Convert the following equations into logarithmicform:
a. 2 = 6x
b. 7 = 6y
c. 9 = 3y
d. X = 8y
2. Convert the followi

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. If a is a positive real number, such that a is not equal to 1, and a^x=b, then what is the logarithmic function?
2. Which of the following equations is correct?
a)log10 (0.1) =1
b)log16 2=4
c)log3 9=2
d)log5 125 =25