Question

Find $x$ if $8^{x-2}\times {\left(\frac{1}{2}\right)}^{4-3x}={\left(0.0625\right)}^x$.

• A. $0$
• B. $4$
• C. $2$
• D. $1$

Answer 1

The correct option is D $1$

$8^{x-2}\times {\left(\frac{1}{2}\right)}^{4-3x}=(0.0625{)}^x$
$\Rightarrow (2^3{)}^{x-2}\times (2^{-1}{)}^{4-3x}={\left(\frac{625}{10000}\right)}^x$
$\Rightarrow 2^{3x-6}\times 2^{-4+3x}={\left(\frac{1}{16}\right)}^x=(2^{-4}{)}^x=2^{-4x}$
$\Rightarrow 2^{3x-6-4+3x}=2^{-4x}$

$\Rightarrow 2^{6x-10}=2^{-4x}$

$\Rightarrow 6x-10=-4x$

$\Rightarrow 10x=10$

$\Rightarrow x=1$