How do you solve #Log(3x+2)-log(2x-1)=log 2#?

1 Answer
Alan P.
Nov 25, 2015

#x=4#

Explanation:

In general #log(a/b) = log(a) - log(b)#

Therefore
#color(white)("XXX")log(3x+2)- log(2x-1) = log((3x+2)/(2x-2))#

So
#color(white)("XXX")log(3x+2)-log(2x+1) = log(2)#

#rArrcolor(white)("XXX")log((3x+2)/(2x-1))= log(2)#

#rArrcolor(white)("XXX")(3x+2)/(2x-1)=2#

#rArrcolor(white)("XXX")3x+2 = 4x-2#

#rArrcolor(white)("XXX")x=4#

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