Find the solution or solutions to each of the following equa

Find the solution (or solutions) to each of the following equations: [round your decimal answers to the nearest hundredth] log_3 (x + 2) -log_3(2x-1) = 2 log_3 (x - 5) + log_3 (x + 1) = 3 (log x)^2 +8 = 6 log x

Solution

a) log₃(x+2) – log₃(2x-1) = 2

log(x+2) – log(2x-1) = 2*log3

log[(x+2)/(2x-1)] = log9

(x+2)/(2x-1) = 9

x + 2 = 18x – 9

17x = 11

x = 0.647

b) log₃(x-5) – log₃(x+1) = 3

log(x-5) – log(x+1) = 3*log3

log[(x-5)/(x+1)] = log27

(x-5)/(x+1) = 27

x - 5 = 27x + 27

26x = -32

x = -1.23

c) (log x)^2 + 8 = 6*log x

     (log x)^2 - 6*log x + 8 = 0

     Let log x = y

      y^2 – 6y + 8 = 0

      y = 4, 2

      log x = 4 ====> x = 54.6

      log x = 2 ====> x = 7.39