Question

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

Answer 1

Answer:

The solution of the given equation is

$x = \frac{9}{1-e^{3} }$

Step-by-step explanation:

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

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

$log (\frac{x+9}{x} ) = 3$  ...(i)

we apply another logarithmic formula

$log^{x} _{e} = y$   then    x  = $e^{y}$

Now From (i) we get

$\frac{x+9}{x} = e^{3}$

On cross multiplication , we get

x +9 = e³ x

x +9 -e³x =0

x (1 - e³) = -9

$x = \frac{-9}{1-e^{3} } = \frac{9}{1-e^{3} }$

Final answer:-

The solution of the given equation is

$x = \frac{9}{1-e^{3} }$

Answer 2

Answer:

decimal form X=0.009

exact form x=1/100

Step-by-step explanation: