Review3 Solutions

Review3 Solutions - Review Sheet 3 Solutions Math 112 Fall...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Review Sheet 3 Solutions Math 112 Fall 2008 1. Graph y = 2 x +1- 3 This graph will have an asymptote of x =- 3 and intercepts (0 ,- 1) and (log 2 3- 1 , 0). 2. Graph y =- log( x- 2) + 2 This graph will have an asymptote of x = 2 and intercepts (0 ,- log(- 2) + 3) and (102 , 0). 3. Graph y = e- x +2- 1 This graph will have asymptote of y =- 1 and intercepts (0 ,e 2- 1) and (2 , 0). 4. Write the expressions as a single logarithm. A) log(6) + log(1 / 3) + log(10) log(20) B) ln(2)- 4(ln(5)- ln(4)) ln 512 625 C) log(4) + 3[log( x- 1)- 2log( x 2- 1)] log 4( x- 1) 3 ( x 2- 1) 6 = log 4 ( x- 1) 3 ( x + 1) 6 5. Write the quantity using sums and differences of the simplest possible logs. A) log x 2- 4 1 2 log( x + 4) + 1 2 log( x- 4) 1 2 B) log 3 q x- 1 2 x +3 1 3 log( x- 1)- 1 3 log(2 x + 3) 6. Write the quantity in terms of ln( x ) and ln( y ): ln xy + ln( x/e 2 )- ln( e 2 x y ) 1 2 ln( x ) + 1 2 ln( y ) + ln( x )- 2- 2- ln( x )- 1 2 ln( y ) = 1 2 ln( x )- 4 7. Solve the following equations: A) log(2 x 2- 4) = 5 2 x 2- 4 = 100000 2 x 2 = 100004 x 2 = 50002 x = 50002 B) (ln( x )) 3 = 3ln( x ) Letting t = ln( x ), we get that t ( t 2- 3) = 0 and hence t = 0 , 3 We disregard the first solution, hence we get x = e 3 ,x = e- 3 C) ln(4)- ln( x ) = (ln(4)) / (ln( x )) Again, let t = ln( x ). Then we have t ln(4)- t 2 = ln(4) and hence t =- ln(4) p (ln(4)) 2 + 4ln(4) 2 But this has complex solutions, which we disregard. Hence there is no solution. D) log( x + 1) = 2 + log( x- 1) 3 log( x + 1)- log( x- 1) = 2 log x + 1 x- 1 = 2 x + 1 x- 1 = 100 x + 1- 100 x + 100 x- 1 = 0- 99 x + 101 x- 1 = 0- 99 x + 101 = 0 99 x = 101 x = 101 99 This answer will result in a positive number inside both of the original logarithms,...
View Full Document

This note was uploaded on 04/29/2009 for the course MATH 112 taught by Professor Carlson during the Fall '08 term at Wisconsin.

Page1 / 11

Review3 Solutions - Review Sheet 3 Solutions Math 112 Fall...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online