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

1.95

Step-by-step 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