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Comprehensive Practice Problems for Solving Logarithmic Equations in Quest 2

This guide presents a series of practice problems and solutions designed to help students master the skills needed to solve logarithmic equations. It includes step-by-step solutions to a variety of logarithmic equations, such as log rules, exponential forms, and solving for variables. Students will find detailed explanations accompanying each problem, enhancing their understanding of logarithmic properties and calculations. Ideal for exam preparation, this resource is tailored to foster confidence in solving logarithmic problems effectively.

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Comprehensive Practice Problems for Solving Logarithmic Equations in Quest 2

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  1. More Practice Problems Review for Quest 2

  2. Solve log52t + log5 (t – 4) = log548 – log5 2 log 5 2t(t – 4) = log 5 (48 / 2) 2t(t – 4) = (48 / 2) 2t2 – 8t =24 2t2 – 8t – 24 = 0 2(t2 – 4t – 12) = 0 2(t – 6)(t + 2) = 0 t = -2, t = 6

  3. Solve 2 log b x = log b 3 + log b ( x + 6 ) log b x2 = log b 3( x + 6 ) x2 = 3( x + 6 ) x2 = 3x + 18 x2 – 3x– 18 = 0 (x – 6) (x + 3) = 0 x = 6, x = -3

  4. P 402 #39 2 log3 (y – 2) – log3 (y – 4) = 2 log 3(y – 2)2= 2 (y – 4) 32 = (y – 2)2 (y – 4) 9 = (y – 2)2 (y – 4) 9y – 36 = y2 – 4y + 4 y2 – 13y + 40 = 0 (y – 5) (y – 8) = 0 Y = 5 , 8 (both )

  5. (64) t = (32) 1 – t (2 6) t = (2 5) 1- t 6 t = 5 – 5t t = 5/11 Solve for the variable.

  6. log 5 625 = x 5 x = 625 5 x = 5 4 x = 4 Rewrite exponentially and solve for x.

  7. (1/27)– 2 p=(3)p+3 (3- 3)– 2 p = (3)p+3 6p = p + 3 5p = 3 p = 3/5

  8. 2 – h = (1/8) 1 – h 2 – h = (2 - 3) 1 – h -h = - 3 + 3h - 4h = - 3 h = 3/4

  9. log 7 1 = x 7 x = 1 7 x = 7 0 x = 0 Find each logarithm.

  10. log 7 7 = x 7 x = 7 7 x = 7 1 x = 1 Find each logarithm.

  11. log 5 5 = x 5 x = 5 ½ x = ½ Find each logarithm.

  12. 9 = r – 2/3 32 = r – 2/3 (32)-3/2 = (r – 2/3)-3/2 3 -3 = r 1/27 = r Solve.

  13. 2x = 5 log2x = log5 x log2 = log5 x = log5 log2 x = log(5)/log(2) x = 2.322 log53.6 = x 5x = 3.6 xlog5 = log3.6 x = log3.6 log5 x = log(3.6)/log(5) x = .796 Solve. Round answers to 3 dec. places

  14. 35 – x = 100 log35 – x = log100 (5 – x)log3= log100 5log3-xlog3=log100 5log3-log100= xlog3 (5log(3)-log(100)) /log(3) x = .808 43 – x = 7x +6 log43 – x = log7x +6 (3 – x)log4 = (x + 6)log7 3log4 – xlog4=xlog7 + 6log7 3log4 – 6log7=xlog7 + xlog4 3log4 – 6log7=x(log7 + log4) 3log4 – 6log7 (log7 + log4) (3log4 – 6log7)/(log7 + log4) – 2.256 Solve. Round answers to 3 dec. places

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