Solve each equation. 1. ANSWER: 16 2. ANSWER: 8 3. MULTIPLE

11.  ANSWER:   −2

7-4 Solving Logarithmic Equations and Inequalities Solve each equation.

12. 

1.  ANSWER:   4

ANSWER:   16 13.  2. 

ANSWER:   9

ANSWER:   8

2

14. log3 (3x + 8) = log3 (x + x) 2

3. MULTIPLE CHOICE Solve log5 (x − 10) = log5 3x. A 10 B2 C5 D 2, 5 ANSWER:   C CCSS STRUCTURE  Solve each equation. 8.  ANSWER:   27

ANSWER:   −2 or 4 2

15. log12 (x − 7) = log12 (x + 5) ANSWER:   4 or −3 2

16. log6 (x − 6x) = log6 (−8) ANSWER:   no solution 2

17. log9 (x − 4x) = log9 (3x − 10) ANSWER:   5

9. 

2

18. log4 (2x + 1) = log4 (10x − 7) ANSWER:   3125

ANSWER:   1 or 4 2

10. 

19. log7 (x − 4) = log7 (− x + 2) ANSWER:  

11.  ANSWER:   −2

ANSWER:   3 35. MUSIC The first key on a piano keyboard corresponds to a pitch with a frequency of 27.5 cycles per second. With every successive key, going up the black and white keys, the pitch multiplies by a constant. The formula for the frequency of the pitch sounded when the nth note up the keyboard is played is given by

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ANSWER:   4

a. A note has a frequency of 220 cycles per second. How many notes up the piano keyboard is this? Page 1 b. Another pitch on the keyboard has a frequency of 880 cycles per second. After how many notes up the

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19. log7 (x − 4) = log7 (− x + 2) ANSWER:   7-4 Solving Logarithmic Equations and Inequalities 3 35. MUSIC The first key on a piano keyboard corresponds to a pitch with a frequency of 27.5 cycles per second. With every successive key, going up the black and white keys, the pitch multiplies by a constant. The formula for the frequency of the pitch sounded when the nth note up the keyboard is played is given by a. A note has a frequency of 220 cycles per second. How many notes up the piano keyboard is this? b. Another pitch on the keyboard has a frequency of 880 cycles per second. After how many notes up the keyboard will this be found? ANSWER:   a. 37 b. 61

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