1. AM6.1b To Define and ApplyLogarithms
AM6.1b To Define and ApplyLogarithms
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“Challenges are what makes life interesting; overcoming them is what makes life meaningful.” -Mark Twain

2. OPENER &LESSON, Start Copying:
There are two kinds of logarithms in your calculator:
Base 10 logs (log) and Base e logs (ln or LN)
The word “log”, when written without a base is understood to be base 10. This is called the “common logarithm”.
The inverse to a log is a power of 10
If you see “ln or LN”, that means natural logs.
ln or LN = loge.
The inverse to ln is a power of e.

3. Active Learning Assignment?

4. The fact that logs and exponents are inverses of each other can be demonstrated by graphs:
D = {x | x > 0}
D = {Reals}
← Notice anything? →
R = {Reals}
R = {f(x) | f(x) > 0}

5. Reads: log, base b, of a equals x
This is what a logarithm looks like: *
anti-log (or exponent’s answer)
exponent
base
Reads: log, base b, of a equals x
Mantra 1: What is the answer to a log?
“The answer to a log is the exponent.”
Mantra 2: What is the key to converting?
“The key to converting is the base.”

6. To convert from logs to exponents:
Since they have a relationship, we can convert from logs to exponents. First, we need some Laws of Logarithms. *
Remember, logs and exponents inverse each other and all that’s left is “a”. *
This can also be said. See calculator
To convert from logs to exponents:
We have a log, and want an exponent.
So, raise both sides to become a power of b
According to rule #1,
exponent
anti-log (or exponent’s answer)
base

7. Let’s try converting some logs to exponents:
Raise both sides to be a power of 3.
Inverse out or “log out”. f f 8 8 e e

8. To convert from exponents to logs:
Now we want to convert from exponents to logs. OK, so we need some more Laws of Logarithms. *
Remember, logs and exponents inverse each other and all that’s left is “x”. *
This can also be said. See calculator
To convert from exponents to logs:
We have an exponent, and want a log.
So, take the logb on both sides.
According to rule #3,
anti-log (or exponent’s answer)
exponent
base

9. Let’s try converting some exponents to logs :
Take the log13 of both sides.
Inverse out or “log out”.

10. Mantra 1: What is the answer to a log?
To reiterate:
base
exponent
anti-log (or exponent’s answer)
Mantra 1: What is the answer to a log?
“The answer to a log is the exponent.”
Mantra 2: What is the key to converting?
“The key to converting is the base.”

11. Simplify: 7 5x 4x 9

12. Active Learning Assignment: Log Conversion Handout 1-16
p , 26a, c; 27a
WOW:
Learn to recognize the inconsequential, then ignore it.