MCQ
If $\frac{3^{5 x} \times 81^2 \times 6561}{2^{2 x}}=3^7$, then $x=$
- A$-\frac{1}{3}$
- B$3$
- ✓$-3$
- D$\frac{1}{3}$
✓
Answer
Correct option: C.
$-3$
$\frac{3^{5 x} \times 81^2 \times 6561}{3^{2 x}}=3^7$
$\Rightarrow 3^{5 x} \times 81^2 \times 6561$
$=3^7 \times 3^{2 x}$
$\Rightarrow 3^{5 x } \times\left(3^4\right)^2 \times 3^8=3^7 \times 3^{2 x }$
$\Rightarrow 3^{5 x +8+8}=3^{7+2 x }$
$\Rightarrow 5 x +16=7+2 x$
$\Rightarrow 5 x -2 x =7-16$
$\Rightarrow 3 x =-9$
$\Rightarrow x =-3$
$\Rightarrow 3^{5 x} \times 81^2 \times 6561$
$=3^7 \times 3^{2 x}$
$\Rightarrow 3^{5 x } \times\left(3^4\right)^2 \times 3^8=3^7 \times 3^{2 x }$
$\Rightarrow 3^{5 x +8+8}=3^{7+2 x }$
$\Rightarrow 5 x +16=7+2 x$
$\Rightarrow 5 x -2 x =7-16$
$\Rightarrow 3 x =-9$
$\Rightarrow x =-3$
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