Please see the attached file for the fully formatted problems.

1. Use the change of base formula to find the following logarithm. Round to five decimals.

2. Solve for x in each of the following equations below. Give the exact answer when possible. If no exact answer is possible, round your answer to 5 decimals.

(a)

(b) log(x + 1) ? log(x ? 4) = log 6 (c) (exact)

3. NO CALCULATOR allowed: Use techniques of transformation and rules of logarithms to find domain, range, intercepts and the equation of the vertical asymptote for the following function:

f(x) = log 5 (x + 2)

a) What action was used to transform y = log 5 (x) into the new function?

g) What are the coordinates of the y-intercept of the new function?

h) Graph:

4. Write the following statement in logarithmic form:

5. Word Problem: Since Bluefin tuna are used for sushi, a prime fish can be worth over $30,000. As a result, the western Atlantic bluefin tuna have been exploited, and their numbers have declined exponentially. Their numbers in 1000s from 1974 to 1991 can be modeled by N(t) = 230(0.881)x , where x stands for years and x = 0 corresponds to 1974.

(a) To the nearest whole number estimate the number of Bluefin tuna in 1974 and 1991.

(b) Find the year when their numbers were 50,000. Set up and solve an appropriate equation.

Logarithmic functions are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

1. Find the derivatives for the following functions ("^" means "to the power of", sorry I can't do double exponents on my keyboard) :
a. f(X) = 100e10X
b. f(X) = e(10X-5)
c. f(X) = e^X3
d. f(X) = 2X2e^(1- X2)
e. f(X) = 5Xe(12- 2X)
f. f(X) = 100e^(X3 + X4)
g. f(X) = e^(200X - X2 + X100)
2. Fi

Please see the attached file for the fully formatted problems.
1. Convert the following equations into logarithmic form:
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

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) = (

A. Convert to logarithmic equations. For example, the logarithmic form 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. An example of an exponential function is y=8^x. Convert this exponential function to a logarithmic function. Plot the graph of both the functions.
2. Graph these two functions
? An exponential function f(x)=6x-2
? A logarithmic function f(x)=log9x
3. Look at the graphical representation below and derive

Many different kinds of data can be modeled using exponential and logarithmicfunctions. For example, exponential functions have been used by Thomas Malthus to describe the growth of human populations. Exponential growth has also been used to indicate how property values grow in strong real estate markets.
For this Discussion

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).