 # 7.6 – Solve Exponential and Log Equations

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7.6 – Solve Exponential and Log Equations

Property of Equality for Exponential Equations
If b is a positive number other than 1, then ___________ if and only if ___________.

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

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

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

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

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

Solve the equation. 5.

Solve the equation. 6.

Solve the equation. 7.

Solve the equation. 8.

Property of Equality for Logarithmic Equations
If b is a positive number other than 1, then __________________ if and only if ___________.

Solve the equation. Check for extraneous solutions.
9. 5x + 9 = 6x 9 = x

Solve the equation. Check for extraneous solutions.
10. 5x + 18 = 7x – 8 18 = 2x – 8 26 = 2x x = 13

Solve the equation. Check for extraneous solutions.
11. 12x – 11 = 3x + 16 9x – 11 = 16 9x = 27 x = 3

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

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

Solve the equation. Check for extraneous solutions.
13. x – 6 = 25 25 = 32 x – 6 = 32 x = 38

Solve the equation. Check for extraneous solutions.
14. 42 = 16 8x = 42 8x = 16 x = 2

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

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