How do you solve #ln(x+2) - ln(x-2) = ln3#?

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Answer 1 · 2016-09-23T15:02:52

#x=4#, is the Soln.

#ln(x+2)-ln(x-2)=ln3#

Since, #lna-lnb=ln(a/b)#, we have,

#ln((x+2)/(x-2))=ln3#

We know that, #ln# is #1-1# function, so, we get,

#(x+2)/(x-2)=3#.

By Compodando-Dividando,

#((x+2)+(x-2))/((x+2)-(x-2))=(3+1)/(3-1)#

#:. (2x)/4=x/2=4/2=2#

#:. x=4#

We see that this root satisfy the given eqn.hence,

#x=4#, is the Soln.