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**7.6 – Solve Exponential and Log Equations**

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**Property of Equality for Exponential Equations**

If b is a positive number other than 1, then ___________ if and only if ___________.

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Solve the equation. 1. 3x – 4 = 5 3x = 9 x = 3

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Solve the equation. 2. 3x – 8 = 4(13 – 3x) 3x – 8 = 52 – 12x 15x – 8 = 52 15x = 60 x = 4

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Solve the equation. 3. 3(4x – 1) = 2(3x + 8) 12x – 3 = 6x + 16 6x – 3 = 16 6x = 19

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Solve the equation. 4. 2x = –(x – 3) 2x = –x + 3 3x = 3 x = 1

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How to solve for a power To eliminate the power, take the log of both sides. It lowers the exponent.

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Solve the equation. 5.

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Solve the equation. 6.

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Solve the equation. 7.

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Solve the equation. 8.

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**Property of Equality for Logarithmic Equations**

If b is a positive number other than 1, then __________________ if and only if ___________.

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**Solve the equation. Check for extraneous solutions.**

9. 5x + 9 = 6x 9 = x

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**Solve the equation. Check for extraneous solutions.**

10. 5x + 18 = 7x – 8 18 = 2x – 8 26 = 2x x = 13

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**Solve the equation. Check for extraneous solutions.**

11. 12x – 11 = 3x + 16 9x – 11 = 16 9x = 27 x = 3

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**12. No solution 3x – 10 = 14 – 5x 8x – 10 = 14 8x = 24 x = 3**

Solve the equation. Check for extraneous solutions. 12. No solution 3x – 10 = 14 – 5x 8x – 10 = 14 8x = 24 x = 3

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How to solve for a Log To eliminate the log, raise both sides to the base power. This eliminates the log. b b

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**Solve the equation. Check for extraneous solutions.**

13. x – 6 = 25 25 = 32 x – 6 = 32 x = 38

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**Solve the equation. Check for extraneous solutions.**

14. 42 = 16 8x = 42 8x = 16 x = 2

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**Solve the equation. Check for extraneous solutions.**

15. 43 = 64 x(x + 12) = 43 x2 + 12x = 64 x2 + 12x – 64 = 0 (x + 16)(x – 4) = 0 x 16 x x = 4, -16 -4

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**Solve the equation. Check for extraneous solutions.**

16. 102 = 100 5x(x – 1) = 102 5x2 – 5x = 100 5x2 – 5x – 100 = 0 5(x2 – x – 20) = 0 x -5 5(x – 5)(x + 4) = 0 x 4 x = 5, -4

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