Question

if $8^x=\frac{64}{2^x}$, then find the value of $x$

Answer 1

$8^x=\frac{64}{2^x}$

$\Rightarrow 2^{3x}=\frac{64}{2^x}$

$\Rightarrow 2^{3x}\times 2^x=2^6$

$\Rightarrow 2^{4x}=2^6$

Since bases are same, we can equate the powers

$\therefore 4x=6$

$\Rightarrow x=\frac{6}{4}=\frac{3}{2}$

$\therefore x=\frac{3}{2}$