Question
Solve for $x:3 \times 7^x = 7 \times 3^x$
✓
Answer
$3 \times 7^x=7 \times 3^x$
$ \Rightarrow \frac{7^x}{7}=\frac{3^x}{3}$
$\Rightarrow 7^{x-1}=3^{x-1} \ldots \ldots ($Using $a^m \div a^n=a^{m-n}) $
$ \Rightarrow 7^{x-1}=3^{x-1} \times 1 $
$ \Rightarrow 7^{x-1}=3^{x-1} \times 7^0 \ldots \ldots($Using $a^0=1)$
$ \Rightarrow x-1=0 $
$ \Rightarrow x=1$
$ \Rightarrow \frac{7^x}{7}=\frac{3^x}{3}$
$\Rightarrow 7^{x-1}=3^{x-1} \ldots \ldots ($Using $a^m \div a^n=a^{m-n}) $
$ \Rightarrow 7^{x-1}=3^{x-1} \times 1 $
$ \Rightarrow 7^{x-1}=3^{x-1} \times 7^0 \ldots \ldots($Using $a^0=1)$
$ \Rightarrow x-1=0 $
$ \Rightarrow x=1$
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