The number of solutions of log(2x)=2log(4x-15)is?

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Answer 1 · 2018-04-29T08:31:02

#x=9/2# =>One real solution.

#log(2x)=2log(4x-15)#

#2log(4x-15)-log(2x)=0#

#log(4x-15)^2-log(2x)=0#

#log[(16x^2-120x+225)/(2x)]=0#

#(16x^2-120x+225)/(2x)=10^0=1#

#16x^2-120x+225=2x#

#16x^2-122x+225=0#

#16x^2-72x-50x+225=0#

#8x(2x-9)-25(2x-9)=0#

#(8x-25)(2x-9)=0#

#x=25/8, 9/2# => reject #x=25/8#, since it makes 4x -15 a

negative number thus causing an undefined status.

#x=9/2# the only valid solution.