Question

Solve $9^{4x}÷3^{2x}=2187$ and find the value of x.

• A. $x=\frac{6}{7}$
• B. $x=\frac{-7}{6}$
• C. $x=\frac{7}{6}$
• D. $x=\frac{-6}{7}$

Answer 1

The correct option is C $x=\frac{7}{6}$

$9^{4x}÷3^{2x}=2187$
$\Rightarrow 3^{2\left(4x\right)}÷3^{2x}=2187$
$\Rightarrow 3^{8x}÷3^{2x}=3^7$
$\Rightarrow 3^{8x-2x}=3^{6x}=3^7$
[$a^m÷a^n=a^{m-n}$]
Since the bases are same, exponents should also be equal
$\therefore 6x=7$
$\Rightarrow x=\frac{7}{6}$