Question

Can you please help me with this question?
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If there is no solution, enter NO SOLUTION.)
ln(x + 5) – ln(x – 3) = ln(x)

Answer 1

I think you meant

log a - log b = log(a/b)

Answer 2

But when you subtract, isn't the original one supposed to be in division form?
log(a/b) = log (a) - log (b)

Answer 3

@tcarroll010 I used the law but it didnt work

Answer 4

OMG! *KILL ME*

Answer 5

thanks for the correction. @tcarroll010

Answer 6

no sweat, all you did was a mental slip. I did one earlier. We all do.

Answer 7

(:

Answer 8

And then,

ln [(x + 5)/(x - 3)] = ln 3

Then put e^ for each side.

e^(ln x) = x

Answer 9

Can you please show me the steps?

Answer 10

e^(ln [(x + 5)/(x - 3)]) = e^(ln 3)

gives

(x + 5)/(x - 3) = 3

and then you can maybe solve from there.

Answer 11

I made a typo:

ln [(x + 5)/(x - 3)] = ln x

Then put e^ for each side.

e^(ln [(x + 5)/(x - 3)]) = e^(ln x)

gives

(x + 5)/(x - 3) = x

and then you can maybe solve from there.

Answer 12

i did, i got x=5 and -1

Answer 13

Good job! Well done! Even with my initial typo!

Answer 14

but I checked they were not right though

Answer 15

That's right, you can only have x = 5 because you can't have a ln of a negative number.

Answer 16

oh ok, thank you! will put that in and see what happens!

Answer 17

When we came down to the equation

(x + 5)/(x - 3) = x

we came to that by power of e. The original equation had a ln x, so we have to put a restriction on x to be positive.

Answer 18

thank god, thank you so much carrol! I got it right, I just had a chance left, if I put in somethign instead of 5 then there would've be no more chances left for me to try other solutions!

Answer 19

Well that worked out well for you!

Answer 20

Thank you so much!! :)

Answer 21

And you are quite welcome!