Question
Solve for $x : \log (x^2 - 21) = 2.$
✓
Answer
$ \log \left(x^2-21\right)=2$
$ \Rightarrow \log \left(x^2-21\right)=\log 100$
$ \Rightarrow x^2-21-100=0$
$ \Rightarrow x^2-121=0$
$ \Rightarrow x^2=121$
$ \Rightarrow x= \pm \sqrt{121}$
$ \Rightarrow x= \pm 11$
$ \Rightarrow \log \left(x^2-21\right)=\log 100$
$ \Rightarrow x^2-21-100=0$
$ \Rightarrow x^2-121=0$
$ \Rightarrow x^2=121$
$ \Rightarrow x= \pm \sqrt{121}$
$ \Rightarrow x= \pm 11$
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