I have work through the whole problem, but I cannot get passed the last step.
The original equation was: $\log(x+2) - \log(x) = 3$
I worked it out to this: $\frac{x+2}{x} = 1000$.
I know the answer is $\frac{2}{999}$ but I don't know how to get there. It's probably really simple, but I am just drawing a blank! Any help would be just great, thanks!
You are almost there!. While: $$\frac{x+2}{x}=1000\to x+2=1000x\to 1000x-x=2\to 999x=2\to x=\frac{2}{999}$$
Multiply both sides by $x$ to find
$$x + 2 = 1000x$$
Subtract $x$ from each side to get
$$2 = 1000x - x$$
Can you take it from there?
$\dfrac{x+2}{x} = 1000$
Dividing both the terms in numerator by x
$\dfrac{x}{x} + \dfrac{2}{x} = 1000$
$1 + \dfrac 2x = 1000$
Subtracting 1 from both side
$1 - 1 + \dfrac 2x = 1000 -1$
$\dfrac 2x = 999$
Multiplying both side by x
$\dfrac 2x \cdot x= 999x$
x cancel out leaving just 2 on left hand side and 99x on right hand side
$2 = 999x$
Therefore the final answer is
$$x = \dfrac{2}{999}$$
