[2] If 2^{2n-1}=\dfrac{1}{8^{n-3}}, then the value of n is:

For Competitive Exams

If $2^{2n-1}=\dfrac{1}{8^{n-3}}$, then the value of n is:

-2

Explanation:

$2^{2n-1}=\dfrac{1}{8^{n-3}}$

$\Leftrightarrow 2^{2n-1}=\dfrac{1}{\left(2^{3}\right)^{n-3}}$

$\Leftrightarrow 2^{2n-1}=\dfrac{1}{2^{3}\left(^{n-3}\right)}$

$\Leftrightarrow 2^{2n-1}=\dfrac{1}{2\left(^{3n-9}\right)}$ $=2^\left({9-3n}\right)$

$\Leftrightarrow 2n-1$ $=9-3n$

$\Leftrightarrow 5n=10$

$\Leftrightarrow n=2$

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