Victory for the ACT Student Text 15e

L ESSON 2 | A LGEBRA AND F UNCTIONS • 217 Which of the following expressions is equivalent to 2 6 x x x 2 + − − ? A. 2 3 x x 2 B. 2 x

2 i i ? 6

_

11.

Manipulating Expressions Involving Exponents Items #8–9

x y x y

2 3

9

Throwback to Math Class Remember to apply the distributive property to terms in parentheses. In item #8, be sure to distribute the exponent of 6 and 2 to all elements contained in the parentheses, including …‘‡ˆϐ‹…‹‡–•Ǥ

8.

_

6 9

3 F. 1 G. 3 H. x y 2 3 J. x y 3 2 3 K. x y 12 12

2 C. 2 x D. 3 x E. x

Factoring Expressions Items #10–12

Throwback to Math Class In general, the difference of two squares x y 2 2 factors into ( x y ) ( x y ). Item #10 demonstrates that knowing the difference of two squares can save time on the exam. Throwback to Math Class A logarithm is the inverse of an exponential function. In the exponential function y b x , the inverse is log y x b . This can be read as “ b needs to be raised to what power x in order to get y ?” Make sure you know these logarithm basics: log b x b x log 1 0 b log 0 undefined b Logarithmic Expressions Items #13–14

12. Which of the following is the factorization of 6 4 2 x x 2 + − ? F. (6 1) ( 3) x x + − G. (6 3) ( 1) x x + − H. (3 1) (2 2) x x J. (2 2) (3 1) x x + − K. (2 4) (3 2) x x + − 13. Evaluate log 125 log 2 1 5 2 c m . A. –1 B. 0 C. 1 D. 2 E. 3 14. If log x m b and log y n b , then log xy ? b F. m n G. bmn H. bxy J. m – n K. mn Throwback to Math Class Memorize these properties: Product Property of Logs: log log log xy x y b b b = + ^ h Quotient Property of Logs: log log log y x x y b b b = − c m Power Property of Logs: log log x y x b y b ^ h Be careful: a common mistake students make is assuming that log( x y ) log( x ) log( y ). This is incorrect! We cannot split apart the ( x y ) expression.

?

1 ` j −

3

−

2 − + + =

9.

2 4 2 2 2 2 0 2

A. 2 2 B. 2 2 C. 2 2 D. E. 2 2 F. x y 2 2 G. x y 2 2 H. x y 2 J. x y 2 K. x y

1

4

1

4

1

4 5

4

Which of the following expressions is equivalent to x y x y 2 2 + − ?

10.

Throwback to Math Class Let’s review the rules for exponents: 1. x x x m n m n = + ^ h 2. x x x n m m n = − 3. x x m n m n ^ ] h g 4. x y m m n _ i 7 A x y mn mn _ i 5. y x y x m m n mn mn f p