solve for x and show steps: log(x-2)-logx=3

Question

amistre64 · Answer

we solved for x in the other question; its 8 .... right?

amistre64 · Answer

log is 10 base here right?

anonymous · Answer

yeah log base 10

amistre64 · Answer

$$10^{(log(x-2)-log(x))}=10^3$$
$$\frac{10^{log(x-2)}}{10^{log(x)}}=10^3$$
$$\frac{x-2}{x}=1000$$

amistre64 · Answer

$$\frac{x-2}{x}=1000$$
$$\frac{x}{x}-\frac{2}{x}=1000$$
$$1-\frac{2}{x}=1000$$
$$-\frac{2}{x}=999$$
i think its right, but that looks peculiar

anonymous · Answer

thats what i got but i wasnt sure. i did it a different way too

amistre64 · Answer

its about -.104791  if it is

amistre64 · Answer

different ways are good, i tend to try to show that math aint got to be done in one specific move

anonymous · Answer

when you plug x back in, does it make the equation equal?

amistre64 · Answer

cant tell yet :)  i havent tried to compute it

amistre64 · Answer

log(x-2)/x =3

10^log(x-2)/x =10^3

(x-2)/x = 1000

x-2 = 1000x

-2 = 999x

x = -2/999

amistre64 · Answer

ugh, cant have x = a negative number for starters

anonymous · Answer

true i forgot about that

amistre64 · Answer

but wolfram gives the answer as a negative too , so i dunno

anonymous · Answer

would it be no solution?

amistre64 · Answer

anonymous · Answer

okay so is the answer x=-2/999 or no solution?

amistre64 · Answer

im going with -2/999

anonymous · Answer

alright thanks