Question

${\left(\frac{12}{17}\right)}^6\times {\left(\frac{289}{144}\right)}^{2x-9}={\left(\frac{17}{12}\right)}^8$, the value of x is:

• A. 12
• B. 9
• C. 8
• D. 6

Answer 1

The correct option is C 8

${\left(\frac{12}{17}\right)}^6\times {\left(\frac{289}{144}\right)}^{2x-9}={\left(\frac{17}{12}\right)}^8$
$\Rightarrow {\left(\frac{17}{12}\right)}^{-6}\times {\left(\frac{17}{12}\right)}^{4x-18}={\left(\frac{17}{12}\right)}^8$
$\Rightarrow {\left(\frac{17}{12}\right)}^{4x-18-6}={\left(\frac{17}{12}\right)}^8$
$\Rightarrow 4x-24=8$
$\Rightarrow 4x=32\Rightarrow x=8$