Solve for x and state exact form

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2log2(x)+log2(x+3) = log2(x)+log2(21-x)

Oct 13th, 2015

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2log2(x)+log2(x+3) = log2(x)+log2(21-x)

log2(x^2)+log2(x+3)=log2(x)+log2(21-x)

log2(x^2*(x+3))=log2(x*(21-x))

x^2*(x+3)=x*(21-x)

x^3+3x^2=21x-x^2

x^3+4x^2-21x=0

x(x^2+4x-21)=0

x(x+7)(x-3)=0

x=0, x=-7, x=3

log2(0) and log2(-7) not exist

answer is x=3

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 13th, 2015

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