Question

n(x+5)=ln(x-1)-ln(x+1)
solve the logarithmic function algebraically. round the result to three decimal places.

Answer 1

ok, what is ln a + ln b equal to?

Answer 2

ln a + ln b = ...what?

Answer 3

lnc?

Answer 4

ln a + ln b = ln(ab)

ln a - ln b = ... what?

Answer 5

ln a-ln b= ln a divided by b?

Answer 6

ln a - ln b = ln(a/b) yes

Last identity before we solve your problem. If
ln p = ln q
what can we say about p and q?

Answer 7

umm they can be multiplied or divide? idk

Answer 8

If
ln p = ln q
then
p = q

Answer 9

Now, your problem:

ln(x+5)=ln(x-1)-ln(x+1)

Using the identity we wrote down above, what is

ln(x-1)-ln(x+1) = ... ?

Answer 10

lnx-1/lnx+1?

Answer 11

No.

ln a - ln b = ... what?

Answer 12

ln(a/b)

Answer 13

ln a - ln b = ln(a/b).

hence

ln(x-1)-ln(x+1) = ... what?

Answer 14

ln(x-1/x+1)?

Answer 15

Yes. Now
\[ \ln(x+5)=\ln(x-1) - \ln(x+1) = \ln ( \frac{x-1}{x+1} ) \]
which implies
\[ x + 5 = \frac{x-1}{x+1} \]

Now solve for x.

Answer 16

ok thank yu so much