Logarithms
What is a logarithm? Name each part of the logarithm
log_10(100) = 2
The inverse of an exponent
10 = base
100 is what we are looking to get to
2 is the exponent needed on base to get to what is inside our log
What is an exponent? Give an example of what it does.
Base = what we multiply
Exponent = how many times we multiply the base by itself
so 5^3 = 5 * 5 * 5
5 is the base
3 is the exponent
Explain the difference between congruence and similarity.
Congruent = same size and shape
Similar = same shape
In what cases can you use Sine and Cosine rule?
When the triangle is not a right angled triangle
What does it mean if the base of a log is not shown? What is the log is written as ln instead.
log = base 10
ln = base e
Name and list all exponent rules.
product
quotient
power
power of a power
power of a product
power of a quotient
fractional exponent
negative exponent
SSA
SAS
AAS
RHS
What does it mean if we have an ambiguous case when using the Sine rule?
It means there are two possible triangles.
What are the main methods we use to solve logarithmic equations?
1. Comparing the insides
2. Convert to exponential form
Solve the following exponential equation.
(125/216)^(-x/4) xx (6/5)^(3x-3)
x = 4/3
True of False. We can use the ratio of lengths, area and volume for any type of similar figure.
true
Give a case where we would use Cosine rule instead of Sine rule.
2 sides and an included angle
3 sides
Explain what the change of base rule is used for.
We use the change of base rule to change the base of our logarithm. This allows us to then apply our log rules to the logarithms.
Illustrate through an example why the product rule is true.
3 * 3 * 3 x 3 * 3 * 3 = 3^6
State the relationship between the ratio of lengths, ratio of area and ratio of volume.
volume is cubed
Simplify the following to a single logarithm.
log_a(y)^2x-3 + log_a(y)^5x-2 - log_a(y)^x-5 -2log_a(y)^3x+3
log_a(1/y^2)
Name 3 real life application where we can use an exponential equation to model the situation.
2. population
3. bacteria
True or False. If two shapes are congruent, then both shapes are inherently similar.
True
Explain the steps needed to identify the ambiguous case when using the Sine rule.
1.2 sides and a non included angle
2.given angle is acute
3.side opposite the angle is less than the other given side
4.the side opposite the given angle is greater than the height of the triangle