Question

If ${\left(\frac{3}{5}\right)}^{2x}=1$, Then find $x$

Answer 1

${\left(\frac{3}{5}\right)}^{2x}=1$

Taking $\log$ both sides, we get

$\log {\left(\frac{3}{5}\right)}^{2x}=\log 1$

$\Rightarrow 2x\log \frac{3}{5}=\log 1$ using $\log a^m=m\log a$

We know that $\log 1=0$

$\Rightarrow 2x[\log 3-\log 5]=0$ using $\log \frac{a}{b}=\log a-\log b$

$\therefore 2x=0$ or $x=0$