How do you solve # ln (x – 2) + ln (x + 2) = ln 5#?

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Answer 1 · 2016-06-09T11:55:19

x=-3 or x=3

Using the property that says :

# ln(a) +ln(b) = ln(a*b)#
We have:

#ln(x-2)+ln(x+2) = ln5#

#ln((x-2)*(x+2)) = ln5#

Rasing exponential both sides we will have:

#(x-2)*(x+2) =5 #

Applying polynomial property on the equation above that says:

# a^2 - b^2 = (a-b)*(a+b)#

We have: #(x-2)*(x+2) = x^2-4#

So,
#x^2 - 4 = 5 #
#x^2 - 4 -5 =0#
#x^2 - 9 =0#
#(x-3)*(x+3)=0#

So,
#x-3=0# thus #x=3#

Or,

#x+3=0# thus #x=-3#