Question
Solve for $\mathbf{x}$, if $: \log _x 49-\log _x 7+\log _x \frac{1}{343}+2=0$
✓
Answer
$ \log _x 49-\log _x 7+\log _x \frac{1}{343}=-2$
$ \Rightarrow \log _x \frac{49}{7 \times 343}=-2$
$ \Rightarrow \log _x \frac{1}{49}=-2$
$ \Rightarrow-\log _x 49=-2$
$ \Rightarrow \log _x 49=2$
$\Rightarrow 49=x^2 \ldots [$Removing logarithm$]$
$\therefore x=7$
$ \Rightarrow \log _x \frac{49}{7 \times 343}=-2$
$ \Rightarrow \log _x \frac{1}{49}=-2$
$ \Rightarrow-\log _x 49=-2$
$ \Rightarrow \log _x 49=2$
$\Rightarrow 49=x^2 \ldots [$Removing logarithm$]$
$\therefore x=7$
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