Victory for the ACT Student Text 15e

220 • M ATH

If x 2 1 1 4 + − = A. –5 B. –1 C. 1 D. 12 E. 24

, then x

?

If 8 2 x F. 0 G. 1 H.

, then x

?

25.

x 3 = +

30.

Equations Involving Radical Expressions Items #25–28

3 2 J. 3 K. 2 3

Throwback to Math Class Memorize the following fact for zero, integer, and rational exponents: 1. a 1 0 if a 0 ! 2. a a 1 n n = − 3. a a n n 1 Test-the- Test The test-the-test strategy is quick to use with item #25 because the answer choices are exactly one value. In item #26, the test- the-test strategy is also quick to use, but you need to recognize the overlap between some of the answer choices. Equations Involving Integer and Rational Exponents Items #29–32 Equations Involving Logarithms Items # 33–34

26. Which of the following is the complete solution set for x 3 2 3 4 − − = − ? F. {} G. { }1 H. { }1 J. { , } 1 1 K. { , } 1 2 27. If x x 2 5 2 5 2 − = − , then x ? A. 1 B. 2 C. 28. Which of the following is the complete solution set for x 9 5 2 + = ? F. { ,4 4} G. { }4 2 5 D. 10 E. 15

If 3

, then x

?

1

x 2

31.

81 A. 2 B. 2 3 C. 3 2 D. 3 2 E. 2 3 If 5 5 3 2 = − ^ h 1

, then 5 x

?

x

32.

F. G. H.

125

1

25

H. { }0 J. { }4 K. {}

5 1 J. 5 K. 25

Which of the following is a value of x •ƒ–‹•ϐ‹‡• –Š‡ ‡“—ƒ–‹‘ log x 4 4 ?

that

If 4 64 x 2 = + , then x ? A. 1 B. 2 C. 3 D. 4 E. 5

33.

29.

A. 1 B. 16 C. 160 D. 256 E. 512

Throwback to Math Class Steps for solving radical equations: Step 1: Isolate the radical expression. Eliminate the radical sign by squaring (if a square root) or cubing (if a cube root) both sides of the equation. Solve for the unknown variable. Step 4: Check the solution(s) in the original equation. It is extremely important that you check your answers when dealing with radical equations. Squaring both sides of an equation while solving for x can generate extraneous solutions. Step 2: Step 3:

Which of the following is a value of x –Šƒ– •ƒ–‹•ϐ‹‡• –Š‡ ‡“—ƒ–‹‘ log log 2 16 16 6 + = x x ? F. 2 G. 4 H. 16 J. 32 K. 64

34.