Lesson21

# Lesson21 - Summer MA 15200 Lesson 21 Section 4.2 and...

This preview shows pages 1–4. Sign up to view the full content.

1 Summer MA 15200 Lesson 21 Section 4.2 and Applied Problems Remember the following information about inverse functions. 1. In order for a function to have an inverse, it must be one-to-one and pass a horizontal line test. 2. The inverse function can be found by interchanging x and y in the function’s equation and solving for y . 3. If 1 () , t h e n f ab fba == . The domain of f is the range of 1 f and the range of f is the domain of 1 f . 4. The compositions 11 ( ( )) and ( ( )) f fx f f x −− both equal x . 5. The graph of 1 f is the reflection of the graph of f about the line y x = . Because an exponential function is 1-1 and passes the horizontal line test, it has an inverse. This inverse is called a logarithmic function. I Logarithmic Functions According to point 2 above, we interchange the x and y and solve for y to find the equation of an inverse function. x f xb = exponential function inverse function y = How do we solve for y ? There is no way to do this. Therefore a new notation needs to be used to represent an inverse of an exponential function, the logarithmic function. Definition of Logarithmic Function For 0 and 0 ( 1) log is equivalent to y b b y xx b >> The function ( ) log b f = is the logarithmic function with base b . The equation log b y x = is called the logarithmic form and the equation y x b = is called the exponential form. The value of y in either form is called a logarithm. Note: The logarithm is an exponent. Exponential Form Logarithmic Form y b x = x y b log = argument base exponent exponent base argument In this form, the y value representing the exponent is called a logarithm.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Ex 1: Convert each exponential form to logarithmic form and each logarithmic form to exponential form. 3 8 1 log ) 5 32 log ) 64 1 8 ) 5 25 ) 16 9 4 3 ) 81 3 ) 2 1 2 2 2 1 2 4 = = = = = = f e d c b a 2 1 5 log ) 5 = g II Finding logarithms Remember: A logarithm is an exponent. Ex 2: Find each logarithm. 10 3 20 15 ) log 100,000 log 27 log 1 log 15 a b c d 12 1 log 144 e 72 3 )4 )( 2) )l o g ( 2 )1 2 ) log 200 rp y q x hm x ia p jm n kr s + + =+ = = =
3 4 1 2 3 ) log 64 log 32 log 81 f g h III Basic Logarithmic Properties 1. log 1 b b = Since the first power of any base equals that base, this is reasonable. 2. log 1 0 b = Since any base to the zero power is 1, this is reasonable. The exponential function ( ) or x x f xb y b == and the logarithmic function 1 () l o g o r l o g bb f xx y x are inverses.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 10

Lesson21 - Summer MA 15200 Lesson 21 Section 4.2 and...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online