Question
Find $x,$ if $:\log_7(2x^2- 1) = 2$
✓
Answer
Consider the equation
$ \log _7\left(2 x^2-1\right)=2 $
$ \Rightarrow 7^2=2 x^2-1 $
$ \Rightarrow 7 x 7=2 x^2-1 $
$ \Rightarrow 2 x^2-1-49=0 $
$ \Rightarrow 2 x^2-50=0 $
$ \Rightarrow 2 x^2=50 $
$ \Rightarrow x^2=\frac{50}{2} $
$ \Rightarrow x^2=25 $
$ \Rightarrow x= \pm \sqrt{25}$
$\Rightarrow x=5 .....[ $neglecting the negative value$ ]$
$ \log _7\left(2 x^2-1\right)=2 $
$ \Rightarrow 7^2=2 x^2-1 $
$ \Rightarrow 7 x 7=2 x^2-1 $
$ \Rightarrow 2 x^2-1-49=0 $
$ \Rightarrow 2 x^2-50=0 $
$ \Rightarrow 2 x^2=50 $
$ \Rightarrow x^2=\frac{50}{2} $
$ \Rightarrow x^2=25 $
$ \Rightarrow x= \pm \sqrt{25}$
$\Rightarrow x=5 .....[ $neglecting the negative value$ ]$
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