Question

The value of $x$ that satisfies the function $3^{({\left({\log }_{9}x\right)}^2-\frac{9}{2}\left({\log }_{9}x\right)+5)}=3\sqrt{3}$ is

• A. $3^3$
• B. $3^7$
• C. $3^6$
• D. $3^2$

Answer 1

Answer: (B), (D)

The correct options are
B $3^7$
D $3^2$

$3^{({\log }_{9}x{)}^2-\frac{9}{2}({\log }_{9}x)+5}=3\sqrt{3}=3^{\frac{3}{2}}$
clearly, $x>0$
Equating power of 3 both sides, we get
$({\log }_{9}x{)}^2-\frac{9}{2}({\log }_{9}x)+5=\frac{3}{2}$
$\Rightarrow 2({\log }_{9}x{)}^2-9({\log }_{9}x)+7=0$
$\Rightarrow {\log }_{9}x=1,\frac{7}{2}$
$\Rightarrow x=9,9^{\frac{7}{2}}$
$\Rightarrow x=3^2,3^7$
Ans: $9,3^7$