Question

31 of 32 (6 complete) Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. log (x 31)- log (x-4)=2 Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is (Simplify your answer. Use a comma to separate answer as needed.) O B. There are infinitely many solutions. O C. There is no solution. Click to select and enter your answer(s).

Answer 1

log ₆ ( x+ 31 ) - log ₆ ( x - 4) = 2

applying log properties on left side

log ₆ ( x + 31 ) / ( x - 4 ) = 2

changing logarithmic form to exponential form

( x+ 31 ) / ( x- 4) = 6^2

x + 31 = 36 ( x - 4)

x + 31 = 36x - 144

36x - x = 31 + 144

35x = 175

x = 175/35

x = 5

the solution set is { 5 }