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.