Mathematics, 16.07.2019 00:30 jayjay5246
Which equation can you solve to find the potential solutions to the equation log2x + log2(x – 6) = 4?
Answers: 1
![\text{The domain:}\\x \ \textgreater \ 0\ \wedge\ x-6 \ \textgreater \ 0\\x \ \textgreater \ 0\ \wedge\ x \ \textgreater \ 6\\\\D:x\in(6;\ \infty)\\\\\log_2x+\log_2(x-6)=4\\\\\log_2[x(x-6)]=\log_22^4\iff x^2-6x=16\\\\x^2-2\cdot x\cdot3=16\ \ \ \ |+3^2\\\\\underbrace{x^2-2\cdot x\cdot3+3^2}_{(a-b)^2=a^2-2ab+b^2}=16+3^2\\\\(x-3)^2=25\to x+3=\pm\sqrt{25}\\\\x-3=-5\ \vee\ x-3=5\ \ \ \ |+3\\\\x=-2\notin D\ \vee\ x=8\in D\\\\\ x=8](/tpl/images/0094/3804/8ad75.png)
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Which equation can you solve to find the potential solutions to the equation log2x + log2(x – 6) = 4...
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