![log_4x+\log_4(x+6)=2\\\\\Rightarrow \log_4x(x+6)=2~~~~~~~~~~~~~~~~~~~~[\textup{Using property (i)}]\\\\\Rightarrow x(x+6)=4^2~~~~~~~~~~~~~~~~~~~~~~~[\textup{Using property (ii)}]\\\\\Rightarrow x^2+6x-16=0\\\\\Rightarrow x^2+8x-2x-16=0\\\\\Rightarrow x(x+8)-2(x+8)=\\\\\Rightarrow (x-2)(x+8)=0\\\\\Rightarrow x-2=0,~~~~~x+8=\\\\\Rightarrow x=2,~~-8.](/tpl/images/0931/9332/3357a.png)
What are the potential solutions of log4x+log4(x+6)=2
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