# PP 7.4 - General Logarithmic and Exponential Functions...

This preview shows pages 1–9. Sign up to view the full content.

General Logarithmic and Exponential Functions

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

View Full Document
General Exponential Functions ) ln( by defined is base ith function w l exponentia The number. real any be 0 Let a x x e a a a = a > 1 0<a<1
Different Bases

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

View Full Document
Laws of Exponents x x x xy y x y x y x y x y x b a ab a a a a a a a a b a y x = = = = - + ) ( . 4 ) ( . 3 . 2 . 1 then , 0 , and numbers, real are and If
Proof of Law 4 x x b x a x b x a x b a x ab x x b a e e e e e ab = = = = = + + ) ( : get we definition the Using ) ln( ) ln( ) ln( ) ln( )] ln( ) [ln( ) ln( Students should write the proofs of the other three laws.

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

View Full Document
Derivatives and Integrals + = = = = = = C a a du a dx du a a a dx d x u u a a a x dx d e e dx d a dx d u u u u x a x a x x ) ln( 1 and ) ln( ) ( if Hence, ) ln( )] ln( [ ) ln( ) ln(
Examples 2 3 5 x dx d ) 5 ln( ) 6 ( 5 ) 6 )( 5 ln( 5 ) 3 ( ) 5 ln( 5 2 2 2 3 3 2 3 x x x dx d x x x = = = dx x 2 7 x u du u 2 , 7 2 1 = = C u + = 7 ) 7 ln( 1 2 1 C x + = 2 ) 7 ln( 1 2 1 7

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

View Full Document
Comments 1 : Rule Power - = r r rx x dx d For the Power Rule to apply, x is a variable,
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 16

PP 7.4 - General Logarithmic and Exponential Functions...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online