Question

Solve log (x + 9) - log x = 3. Round to the nearest thousandth if necessary.

Answer 1

decimal form X=0.009

exact form x=1/100

Explanation:

Answer 2

The solution of the given equation is

`x = (9)/(1-e^(3) )`

Explanation:

Given Log(x+9) - log x =3

By using Formula log a -log b = log(a/b)

`log ((x+9)/(x) ) = 3` ...(i)

we apply another logarithmic formula

`log^(x) _(e) = y` then x =
`e^(y)`

Now From (i) we get

`(x+9)/(x) = e^(3)`

On cross multiplication , we get

x +9 = e³ x

x +9 -e³x =0

x (1 - e³) = -9

`x = (-9)/(1-e^(3) ) = (9)/(1-e^(3) )`

Final answer:-

The solution of the given equation is

`x = (9)/(1-e^(3) )`