AM6.1b To Define and ApplyLogarithms 11-19-15 AM6.1b To Define and ApplyLogarithms Got ID? “Challenges are what makes life interesting; overcoming them is what makes life meaningful.” -Mark Twain

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.

Active Learning Assignment?

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}

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.”

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

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

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

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

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.”

Simplify: 7 5x 4x 9

Active Learning Assignment: Log Conversion Handout 1-16 p. 200 23-25, 26a, c; 27a WOW: Learn to recognize the inconsequential, then ignore it.