Question

What is the value of x in the equation ln (x + 6) – ln (2x – 1) = 1?

Answer 1

1.95

Explanation:

hello :

ln (x + 6) – ln (2x – 1) = 1 ...(*)

this expression exist : 2x-1 > 0 and x+6 > 0 means : x> 1/2 and x > -6

hence for : x> 1/2 (*) equivalent to ln((x+6)/(2x-1))= lne.......(1=lne)

(x+6)/(2x-1) = e

x+6 = e(2x-1) means : x+6 = 2ex-e

-x+2ex = e+6

x(2e-1) = e+6

x = (e+6)/(2e-1) =(2.73+6)/(2(2.73)-1) =8.73/4.46 =1.95