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This worksheet consists of a combination of skills including order of operations, integer addition, integer subtraction, matrices, combining like terms, exponents, exponents and division and much more!
Grade: 7th, 8th, 9th, 10th
Domain: Algebra
Type: Worksheet

Become Friends With Logarithms - Instructions, examples, exercises with examples
Notes from website:
Become Friends With Logarithms
Logarithms are actually very easy once you get used to how they behave. After that they are as
predictable as yesterday’s weather. All it takes is practice.
What is a logarithm? A logarithm is an exponent. Specifically, logarithms are written “ x y b log = ”
and read as “the log, base b, of x is y”. It really means “base b, taken to the power y, gives x”.
Hence,
x y b x y
b log = Û =
So, for instance, if you had an unknown variable as an exponent, you’d work out a logarithm to find
that exponent’s value. Here’s an easy example: 2 = 8 x . In this case we know from past experience
that x = 3, since 2 8 3 = . Hence, “3 is the logarithm, base 2, of 8”, or 3 log 8 2 = .
• Practice Set I – Converting from exponential into logarithm form.
In this set, you take a known expression that should be obviously true, and convert it into its
equivalent logarithm form. This will give you practice to see where the proper places are for each
number in the logarithm form.

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Laws, examples and exercises
---------------------- Notes from website ---------------------
Worksheet 2:7 Logarithms and Exponentials
Section 1 Logarithms
The mathematics of logarithms and exponentials occurs naturally in many branches of science.
It is very important in solving problems related to growth and decay. The growth and decay
may be that of a plant or a population, a crystalline structure or money in the bank. Therefore
we need to have some understanding of the way in which logs and exponentials work.
Denition: If x and b are positive numbers and b 6= 1 then the logarithm of x to the base b is
the power to which b must be raised to equal x. It is written logb x. In algebraic terms this
means that
if y = logb x then
x = by
The formula y = logb x is said to be written in logarithmic form and x = by is said to be written
in exponential form. In working with these problems it is most important to remember that
y = logb x and x = by are equivalent statements.
Example 1 : If log4 x = 2 then
x = 42
x = 16
Example 2 : We have 25 = 52. Then log5 25 = 2.
Example 3 : If log9 x = 1
2 then
x = 9
1
2
x = p9
x = 3
Example 4 : If log2
y
3 = 4 then
y
3
= 24
y
3
= 16
y = 16 3
y = 48
Exercises:
1. Write the following in exponential form:
(a) log3 x = 9
(b) log2 8 = x
(c) log3 27 = x
(d) log4 x = 3
(e) log2 y = 5
(f) log5 y = 2
2. Write the following in logarithm form:
(a) y = 34
(b) 27 = 3x
(c) m = 42
(d) y = 35
(e) 32 = x5
(f) 64 = 4x
3. Solve the following:
(a) log3 x = 4
(b) logm 81 = 4
(c) logx 1000 = 3
(d) log2
x
2 = 5
(e) log3 y = 5
(f) log2 4x = 5
Section 2 Properties of Logs
Logs have some very useful properties which follow from their denition and the equivalence
of the logarithmic form and exponential form. Some useful properties are as follows:
logb mn = logbm + logb n
logb
m
n
= logbm

math worksheets - Inequalities and Absolute Value Worksheet 8th grade, 9th grade, high school, college, using negative signs and absolute values
Insert >, < or = into each to make a true statement

Trigonometry worksheets including: Law of Sines, Ambiguous Case of the Law of Sines' Law Of Cosines, Law of Sines and Cosines Worksheet
Grades: 10th, 11th, 12th, High school
Domain: Trigonometry
Type: Worksheets

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y each identity below.
1. cos x + sin x tan x = sec x
2. sec x - cos x = tan x sin x
3. tan x csc x cos x = 1
4. sin2 qI1 + cot2 qM = 1
5. 1
sin t - 1 + 1
sin t + 1 = -2 tan t sec t
6. sin t
csc t + cos t
sec t = 1

Trigonometric Identities

Use a sum or difference formula to find the exact value of each expression.
7. cos (75°) = cos (45° + 30°) =
8. tan (15°) =
9. sin I 5 p
12 M

TrigonometricIdentities

Use the figure to find the exact values of each trigonometric function.
3
4
q
10. sin 2q 11. cos 2q 12. tan 2q
Use the given information to find the exact value of:
a. sin 2q b. cos 2q c. tan 2q
13. sin q = 15
17 , q lies in quadrant II 14. cos q = 24
25 , q lies in quadrant III
Use a half-angle formula to find the exact value of each expression.
15. cos 157.5°
4 Trigonometric Identities .nb
16. sin 105°
17. tan 112.5°
Trigonometric Identities .nb 5