# How do you solve #ln(x) + ln(x-2) = ln(x+4)#?

##### 1 Answer

Oct 21, 2015

Use properties of logs to derive a quadratic equation in

#x = 4#

#### Explanation:

#ln(x+4) = ln(x) + ln(x-2) = ln(x(x-2))#

So

#x+4 = x(x-2) = x^2 - 2x#

Subtract

#0 = x^2-3x-4 = (x-4)(x+1)#

So

Discard

So the only solution is