1.1 Sets of Numbers
Subject:
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Mathematics
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how to solve logs
Subject:
1. To solve a logarithmic equation, rewrite the equation in exponential form and solve for the variable.
Example 1: Solve for x in the equation Ln(x)=8.
Solution:
Step 1: Let both sides be exponents of the base e. The equation Ln(x)=8 can be rewritten .
Step 2: By now you should know that when the base of the exponent and the base of the logarithm are the same, the left side can be written x. The equation can now be written .
Step 3: The exact answer is
and the approximate answer is
Check: You can check your answer in two ways. You could graph the function Ln(x)-8 and see where it crosses the x-axis. If you are correct, the graph should cross the x-axis at the answer you derived algebraically.
solving exponential equations
Subject:
to solve exponential equations without logarithms, you need to have equations with comparable exponential expressions on either side of the "equals" sign, so you can compare the powers and solve. In other words, you have to have "(some base) to (some power) equals (the same base) to (some other power)", where you set the two powers equal to each other, and solve the resulting equation. For example:
Solve 5x = 53.
Since the bases ("5" in each case) are the same, then the only way the two expressions could be equal is for the powers also to be the same. That is:
x = 3
Algebra laws
Subject:
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Algebra 2
Subject:
Tags:
. A subset of the real numbers is closed under addition if, for any two
numbers, a and b, that are members of the subset, the number is also
a member of the subset. Tell whether each of the following subsets of the
real numbers is closed under addition. If it is not, give an example that
shows it is not.
a. The set of whole numbers b. The set of negative integers
c. The set of irrational numbers d. The set of rational numbers
2. For each of the sets in Problem 1, tell whether the set is closed under
multiplication. If it is not, give an example that shows it is not.
3. a. For each of the following pairs of rational numbers, and find the
rational number and write the 3 rational numbers in increasing
order.
(i) (ii) (iii) (iv)
pythagorean theorem
Subject:
a^2 + b^2 = c^2
How to add fractions easilly
Subject:
My Pre-Cal teacher taught us this. When you are trying to add fractions during a sine or cosine problem, or something that has to do with a unit circle or a triangle, use this:
Ex: 1/4 + 3/5
Multiply 5*1, multiply 4*3 and add them for the numberator, and multiply 4*5 for the denominator.
So it would be 5+12/20. 17/20.
You multiply the denominator of one and numerator of other by the denominator of other and numerator of one.Then add. That will give you the numerator. Then the denomnator you multiply both denominators and add.
Implicit Differentiation Simplified
Subject:
y + xy = 7x
Implicit differentiation?
(dy/dx) + (x(dy/dx)+ y(1)) = 7(1)
(dy/dx)(x + 1) = 7 - y
(dy/dx) = (7 - y) / (x + 1)
Easy?
Factor and Remainder Theorem
Subject:
Factor
The expression x-a is a linear factor of a polynomial if and only if the value a is a zero related polynomial function.
Remainder
If a polynomial function P(x) of a degree greater than or equal to 1 is divided by the linear factor (x-a), where a is a constant, then the remainder is P(a)
Factor and Remainder Theorem
Subject:
Factor
The expression x-a is a linear factor of a polynomial if and only if the value a is a zero related polynomial function.
Remainder
If a polynomial function P(x) of a degree greater than or equal to 1 is divided by the linear factor (x-a), where a is a constant, then the remainder is P(a)
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