Solve for x Solve for x ln 3x 4 ln20 lnx5Solutionln3x 4

Solve for x:

Solution

ln(3x- 4) = ln 20 - ln (x -5) = ln 20/ (x -5) ( as log a/b = log a - log b). Then (3x -4 ) = 20/(x -5) or, (3x -4) (x - 5) = 20 or, 3x² - 19x + 20 = 20 or, 3x² - 19x = 0 or, x(3x - 19) = 0 so that either x = 0 or, 3x -19 = 0 so that x = 19/3. Thus, the answer is either x = 0 or, x = 19/3.