Solve the following logarithmic equation In x 4 In x 3 4 S

Solve the following logarithmic equation. In (x+ 4)- In (x - 3) = 4 Select the correct choice below and. if necessary fill in the answer box to complete your choice (Round to four decimal places as needed Use a comma to separate answers as needed.) There is no solution

Solution

We have ln(x+4)- ln (x-3) = 4 or, ln [(x+4)/(x-3)] = 4 ( as loga/b = log a -log b)

Hence (x+4)/(x-3) = e⁴ = 54.59815. Then (x+4) = 54.59815(x-3) or, 54.59815 x - x =3*54.59815 +4 0r, 53.59815 x = 163.79445 +4 = 167.79445. Hence x = 167.79445/53.59815 = 3.055972081 = 3.056(approximately)