Chapter 6 - Logarithms - Keep in Mind

Question 1

What are the two ways they would give you logarithmic equations?

Answer 1

log = number
log = log

Question 2

What is x defined as in logarithmic form? What happens if you manipulate it?
log₃(5) = x

Answer 2

1. Ask yourself: What power of 3 gives me 5?
2. Switch to exponential form: 3ˣ = 5
3. If you add 1 to x, it will multiply 5 by base (3)
4. If you multiply x by 2/3/etc., it will square/cube/quadruple etc. 5

Question 3

What do you do if the coefficient in front of log is a fraction?

Answer 3

Apply root rather than power TO base in parentheses
Ex:1/2 ln (x) -> ln√x

Question 4

What do you do if there is a radical in the denominator of a logarithmic function?

Answer 4

There is no need to rationalize it

Question 5

What are the values of log(1), log(10), and log(100)?

Answer 5

1. Ask yourself what exponent makes base equal to other side?
2. log(1) = 0 (since 10^0 = 1)
3. log(10) = 1 (since 10^1 = 10)
4. log(100) = 2 (since 10^2 = 100)
5. log (1000) = 3 (since 10^3 = 1000)

General Rule:
log(10^n) = n

Question 6

What is the value of lnₑ?
What is the value of lnₑ₂?

Answer 6

1. lnₑ = X
2. 1 (equal to exponent)
3. lnₑ₂ = X
4. 2 (equal to exponent)

Question 7

According to the power rule, how do you convert a square root to an exponent?

Answer 7

Any type of root converted to an exponent that is a fraction (denominator is the type of root, numerator is the power raised)
Ex: Square root is ^1/2

Question 8

What is the end behavior of a logarithmic function? (3)

Answer 8

As x→ ∞, f(x) → ∞
As x→ -∞ f(x) → DNE
As x → 0, f(x) → -∞

Question 9

How do you find the vertical asymptote of a logarithmic function?

Answer 9

Value of x that makes the parentheses equal to 0
Ex: (-x-2) -> x = -2

Question 10

When can you drop logs? (3)

Answer 10

Must be:
- Fully Condensed
- Same Base
- Opposite sides of the equation

Question 11

How can you determine the domain based on an equation of a logarithmic function? (3)

Answer 11

1. X is whatever makes parentheses equal to 0, which is VA
2. If (X +/- ____), X > VA
3. If (___ +/- X), X < VA