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
