Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Review: Logarithmic Functions - GraphicallyLogarithms are the INVERSE of Exponentials

Transformations are the same as any other function, reference Chapter 1.

, x > 0

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Logarithmic functions are the INVERSE of exponential functions

Remember:

1. Switch x and y

2. Remember: logaab = bTo isolate y, take log2 of both sides

3. Write as the inverse function

Logarithmic Functions

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Find the inverse function, f-1:

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Special BasesLogarithms with base 10• "common log"• omit the base instead of log10 x, we

just write log x• y = log x is the inverse of y = 10x • the log key on your calculator is log

base 10

Natural Logarithms• "log base e" is loge x• we write as ln x• your calculator has a ln key!

Make sure to use parentheses carefully and correctly when using logs on

your calculator!

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Remember:

Therefore, if we substitute the exponential function into the inverse

logarithmic function, we get xor

if we substitute the logarithmic function into the inverse exponential

function, we get x

To solve for x, we need to remember that logs and exponentials are inverse functions

Example:

f(x) = 4x+3, g(x) = log4x - 3

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Use these relationships to help solve for x!

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Without a calculator evaluate:

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Let b, m, and n be positive numbers such that b does not equal 1Laws of Logarithms

*These are you in your booklet!*

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

We can derive this key result from the power property law.

All of the laws are true for logs in any base.

*You MUST learn this formula, it is not in the IB SL formula booklet!*or you can ALWAYS use the power property law

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Expanding - is when you go from one log to multiple logs separated by addition, subtraction, multiply by a constant

Examples of Expanding:1. 2. 3.

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Condensing is when you do the reverse - write as ONE log

Examples of Condensing

4. 5. 6.

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

You Try!Expand Condense

1.

2.

3.

4.

5.

6.

7.

8.

log3a + log3b + 2log3c

(1/2)log4x + (1/2)log4y

lnx - (lny + lnz)

4log2x + 4log2y - 2log2z

log3t

log4x5

log4(1/5)

ln (x8/36y3)

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

IB Style Question

Logarithms and Logarithms Laws

IBSLY1 H Block

January 21, 2016

Homework

4K: 1 (c-h) -> <5 mins4L: 1 - 5 (pick 2 from each), 6 - 9 -> 10-15 mins4M: 1(c,d,f,g), 2(c,e,f), 3(b,d,e) -> 10-15 mins

4N: 1 - 6 -> 20-30 mins