MCQ
If $\frac{3^{2\text{x}-8}}{225}=\frac{5^3}{5^{\text{x}}},$ then $x =$
- A$2$
- B$3$
- ✓$5$
- D$4$
✓
Answer
Correct option: C.
$5$
We have to find the value of $x$ provided $\frac{3^{2\text{x}-8}}{225}-=\frac{5^3}{5^\text{x}}$
So,
$\frac{3^{2\text{x}-8}}{225}-=\frac{5^3}{5^\text{x}}$
By cross multiplication we get
$3^{2\text{x}-8}\times5^\text{x}=3^2\times5^2\times5^3$
By equating exponents we get
$3^{2\text{x}-8}=3^2$
$2\text{x}-8=2$
$2\text{x}=2+8$
$2\text{x}=10$
$\text{x}=\frac{10}{2}$
$\text{x}=5$
And
$5^{\text{x}}=5^{3+2}$
$\text{x}=3+2$
$\text{x}=5$
Hence the correct choice is $c.$
So,
$\frac{3^{2\text{x}-8}}{225}-=\frac{5^3}{5^\text{x}}$
By cross multiplication we get
$3^{2\text{x}-8}\times5^\text{x}=3^2\times5^2\times5^3$
By equating exponents we get
$3^{2\text{x}-8}=3^2$
$2\text{x}-8=2$
$2\text{x}=2+8$
$2\text{x}=10$
$\text{x}=\frac{10}{2}$
$\text{x}=5$
And
$5^{\text{x}}=5^{3+2}$
$\text{x}=3+2$
$\text{x}=5$
Hence the correct choice is $c.$
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