How do you solve # log(5x-6) = 2log x#?

1 Answer
May 21, 2016

#x=2# or #x=3#

Explanation:

Note that
#color(white)("XXX") 2log(x)=log(x^2)#

So
#color(white)("XXX")log(5x-6)=2log(x)#
is equivalent to
#color(white)("XXX")log(5x-6)=log(x^2)#

which implies
#color(white)("XXX")5x-6=x^2#

#color(white)("XXX")x^2-5x+6=0#

#color(white)("XXX")(x-2)(x-3)=0#

So either
#color(white)("XXX")(x-2)=0color(white)("XX")rarrcolor(white)("XX")x=2#
or
#color(white)("XXX")(x-3)=0color(white)("xx")rarrcolor(white)("XX")x=3#