LESSON 13.4

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Logging On Solving Logarithmic Equations Problem Set Solve each logarithmic equation. Check your answer(s). 1. log2 (x2 2 x) 5 1

2. log15 (x2 2 2x) 5 1

log2 (x2 2 x) 5 1 21 5 x2 2 x 0 5 x2 2 x 2 2 0 5 (x 1 1)(x 2 2) x 5 21, 2 Check: log2 ( (21)2 2 (21) ) 0 1 log2 (1 1 1) 0 1 log2 2 5 1 log2 (22 2 2) 0 1 log2 (4 2 2) 0 1

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log2 2 5 1

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Skills Practice 4. log2 (x2 1 6x) 5 4

5. log4 (x2 2 12x) 5 3

6. log10 (x2 1 15x) 5 2

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3. log6 (x2 1 5x) 5 2

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8. log4 (2x2 2 28x) 5 3

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7. log3 (3x2 118x) 5 4

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Use the properties of logarithms to solve each logarithmic equation. Check your answer(s). 9. 2 log3 x 2 log3 8 5 log3 (x 2 2)

10. log4 (x 1 3) 1 log4 x 5 1

2 log3 x 2 log3 8 5 log3 (x 2 2) log3 x2 2 log3 8 5 log3 (x 2 2) 2 log3 x  5 log3 (x 2 2) 8

( __ ) __x  5 x 2 2 2

8 x2 5 8x 2 16

x2 2 8x 1 16 5 0 (x 2 4)2 5 0 x 5 4 Check: 2 log3 4 2 log3 8 0 log3 (4 2 2) log3 16 2 log3 8 0 log3 2 log3 16  0 log3 2 8 log3 2 5 log3 2

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( ___ )

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12. log2 x 1 log2 (x 2 6) 5 4

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11. log (2x2 1 3) 1 log 2 5 log 10x

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14. log2 3 1 log2 (3x2 1 4) 5 log2 ( 39x )

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13. 2 log5 x 2 log5 4 5 log5 (8 2 x)

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(

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1 x2 2 6 2 log __ 1 5 log x 16. log4 __ 4 5 4 5

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15 1 ln 2 5 ln (11x) 15. ln x2 1 ___ 2

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