How to tackle ln(x-2)-ln(x+2)=2?

ln(x-2)-ln(x+2)=2

In [(x-2)/(x+2)] = In(e^2)

(x-2)/(x+2) = e^2

x-2 = x(e^2) + 2(e^2)

x[(e^2) - 1] = -2[1 + (e^2)]

x = 2[1 + (e^2)] / [1 - (e^2)]

good old ln's!

ln x - ln y = ln x/y
so
ln(x-2)-ln(x+2)
is the same as

ln(x-2)/(x+2) = 2

the e button or exponential is the opposite of ln, so

e^[ln(x-2)/(x+2)] = e^2
(x-2)/(x+2) = e^2

(x-2) = e^2(x+2)
x-2 = 7.39x + 14.77
x= 7.39x +16.77
6.39x=16.77
x= 2.62

to 2.dp

lnA - lnB = ln(A/B)

therefore

for the eq above

ln[ (x-2)/(x+2) ] = 2

= (x-2)/(x+2) = exp(2)

you can subsequently get x with simple algebra.

ln(x - 2) - ln(x + 2) = 2
ln[(x - 2)/(x + 2)] = 2
(x - 2)/(x + 2) = e^2
x - 2 = e^2(x + 2)
x - 2 = e^2(x) + 2e^2
x - e^2(x) = 2 + 2e^2
x(1 - e^2) = 2(1 + e^2)
x = [2(1 + e^2)]/[(1 + e)(1 - e)]

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

ln( (x-2) / (x+2) ) = 2
e^2 = (x-2) / (x + 2)

e^2 * (x + 2) = x - 2
e^2 * x + 2 * e^2 = x - 2

e^2 * x - x = -2 - 2 * e^2
x * (e^2 - 1) = -2 - 2 * e^2

x = -2 * (1 + e^2) / (e^2 - 1)

Plug that into your calculator

Starting point..
ln(x-2)-ln(x+2)=2
ln((x-2)/(x+2))=2
(x-2)/(x+2) = e^2
and then its simple algebra..!

Tackle? You solve the equation or tackle them?
Use laws of logarithm ( I assume you know them) if you want to solve it. For tackling, consult some one else..