algebrasheet2 solution

# algebrasheet2 solution - 1 Solutions to the Second Algebra...

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

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

View Full Document

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.

Unformatted text preview: 1 Solutions to the Second Algebra Worksheet 1.1 Solve e 2 x- 2 e x- 3 = 0 for x . This is a quadratic problem. Let z = e x . Then, we have that: z 2- 2 z- 3 = 0 ⇒ ( z- 3)( z + 1) = 0 ⇒ z = 3 or z =- 1 ⇒ e x = 3 or e x =- 1 ⇒ x = ln(3) or x = ln(- 1) ⇒ x = ln(3) . 1.2 Solve 1 2 x- 8 x 1 / 3 = 0 for x . This is a factoring problem. 1 2 x- 8 x 1 / 3 = 0 ⇒ x 1 / 3 1 2 x 2 / 3- 8 ¶ = 0 ⇒ x 1 / 3 = 0 or 1 2 x 2 / 3- 8 = 0 ⇒ x = 0 or x 2 / 3 = 16 ⇒ x = 0 or x = 16 3 / 2 ⇒ x = 0 or x = 4 3 ⇒ x = 0 or x = 64 . 1.3 Solve 2 x = 3 e 4 x for x . With problems involving things being raised to the x power it is a good idea to try to use logs. Just be sure to use the properties correctly!! 2 x = 3 e 4 x ⇒ ln(2 x ) = ln(3 e 4 x ) ⇒ x ln(2) = ln(3) + ln( e 4 x ) ⇒ x ln(2) = ln(3) + 4 x ⇒ x ln(2)- 4 x = ln(3) ⇒ x (ln(2)- 4) = ln(3) ⇒ x = ln(3) ln(2)- 4 . 1.4 Solve 1- 1 1+ x = k for x . Whenever what you are solving for appears in the denominator of a fraction it is a good idea to “clear” the fraction by multiplying by the denominator. 1- 1 1 + x = k ⇒ (1 + x ) 1- 1 1 + x ¶ = k (1 + x ) ⇒ 1 + x- 1 = k + kx ⇒ x = k + kx ⇒ x- kx = k ⇒ x (1- k ) = k ⇒ x = k 1- k 1.5 Solve e x- 2 = k 4 x for x . e x- 2 = k 4 x ln( e x- 2 ) = ln( k 4 x ) x- 2 = ln( k ) + ln(4 x ) x- 2 = ln( k ) + x ln(4) x- x ln(4) = ln( k ) + 2 x (1- ln(4) = ln( k ) + 2 x = ln( k ) + 2 1- ln(4) . 1.6 Solve 4 x 3 e kx- 16 xe kx = 0 for x . 4 x 3 e kx- 16 xe kx = 0 4 xe kx ( x 2- 4) = 0 4 xe kx ( x- 2)( x + 2) = 0 4 x = 0 or or e kx = 0 or x- 2 = 0 or x + 2 = 0 ⇒ x = 0 or or kx = ln(0) or x = 2 or x =- 2 ⇒ x = 0 or x = 2 or x =- 2 . 1.7 Solve 2 ln(5 x ) = ln( x + 2) for x ....
View Full Document

## This note was uploaded on 03/12/2012 for the course MATH 161 taught by Professor C during the Fall '07 term at Arizona.

### Page1 / 11

algebrasheet2 solution - 1 Solutions to the Second Algebra...

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

View Full Document
Ask a homework question - tutors are online