Answer:
x=5
Step-by-step explanation:
Given equation is
[tex]\log\left(x\right)+\log(x-2)=\log(3x)[/tex]
Apply formula: [tex]\log A+\log B=\log\left(AB\right)[/tex]
[tex]\log\left(x(x-2)\right)=\log(3x)[/tex]
[tex]\log\left(x^2-2x)\right)=\log(3x)[/tex]
Since both sides have equal bases so we can drop the log
[tex]x^2-2x=3x[/tex]
[tex]x^2-2x-3x=0[/tex]
[tex]x^2-5x=0[/tex]
[tex]x(x-5)=0[/tex]
Which gives x=0 and x-5=0
or x=0 and x=5
Original problem [tex]\log\left(x\right)+\log(x-2)=\log(3x)[/tex] is not defined at x=0 henc only x=5 is the final answer.
