Answer:
x = 1 , -6
Step-by-step explanation:
given,
ln (x + 2) = ln (12) − ln (x + 3)
using identity of logarithm
ln (ab) = ln (a) + ln (b)
ln (a) - ln(b) = ln (a/b)
now
ln (x + 2) = ln (12) − ln (x + 3)
ln (x + 2) = [tex]ln (\dfrac{12}{x+3})[/tex]
on comparing
[tex]x + 2 = \dfrac{12}{x+3}[/tex]
(x+2)(x+3) = 12
x² + 5 x + 6 = 12
x² + 5 x - 6 = 0
x² + 6 x - x - 6 = 0
x(x + 6) -1 (x+ 6) = 0
(x - 1)(x + 6) = 0
x = 1 , -6
Hence, the value of x comes out to be x = 1 , -6
