Solving the following logarithmic equation In x 3 In x 6

Solving the following logarithmic equation. In (x + 3)- In (x - 6) = 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x = (Round to four decimal places as needed. Use a comma to separate answers as needed.) There is no solution.

Solution

We have ln(x+3)–ln(x-6) = 2 or, ln [(x+3)/(x-6) ]=2 so that (x+3)/(x-6) = e² = 7.3890561 [ as ln a –ln b = ln (a/b)]

Then, on multiplying both the sides by (x-6) ( if x 6), we get x+3 =7.3890561( x-6) or, x+3 =7.3890561x – 44.3343366 or, 6. 3890561x = 47. 3343366 so that x = 47. 3343366/6. 3890561 = 7.408658785 or, x = 7.4087 ( on rounding off to 4 decimal places).