MCQ
If $\frac{3^{5\text{x}}\times81^2\times6561}{3^{2\text{x}}}$ then $x =$
- A$3$
- ✓$-3$
- C$\frac{1}{3}$
- D$-\frac{1}{3}$
✓
Answer
Correct option: B.
$-3$
We have to find the value of x provided $\frac{3^{5\text{x}}\times81^2\times6561}{3^{2\text{x}}}=3^7$
So,
$\frac{3^{5\text{x}}\times81^2\times6561}{3^{2\text{x}}}=3^7$
By using law of rational exponents we get
$3^{5\text{x}+8+8-2\text{x}}=3^7$
By equating exponents we get
$5\text{x}+88-2\text{x}=7$
$3\text{x}+16=7$
$3\text{x}=7-16$
$3\text{x}=-9$
$\text{x}=\frac{-9}{3}$
$\text{x}=-3$
Hence the correct choice is $b.$
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