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
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. 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)
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
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) = (
Common and Natural Logarithms
1. For the exponential function ex andlogarithmic 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).
Many different kinds of data can be modeled using exponentialandlogarithmicfunctions. For example, exponentialfunctions 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.
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