MCQ
If $9^{x+2}=240+9^x$, then $x =$
- ✓$0.5$
- B$0.2$
- C$0.4$
- D$0.1$
✓
Answer
Correct option: A.
$0.5$
We have to find the value of $x$
Given $9^{x+2}=240+9^x$
$9^x \times 9^2=240+9^x$
$9^2=\frac{240}{9^{\text{x}}}+\frac{9^{\text{x}}}{9^{\text{x}}}$
$81=\frac{240}{9^{\text{x}}}+1$
$81-1=\frac{240}{9^\text{x}}$
$80=\frac{240}{9^\text{x}}$
$9^\text{x}\times80=240$
$9^\text{x}=\frac{240}{80}$
$3^{2\text{x}}=3$
$3^{2\text{x}}=3^1$
By equating the exponents we get
$2\text{x}=1$
$\text{x}=\frac{1}{2}$
$\text{x}=0.5$
Hence the correct alternative is $a.$
Given $9^{x+2}=240+9^x$
$9^x \times 9^2=240+9^x$
$9^2=\frac{240}{9^{\text{x}}}+\frac{9^{\text{x}}}{9^{\text{x}}}$
$81=\frac{240}{9^{\text{x}}}+1$
$81-1=\frac{240}{9^\text{x}}$
$80=\frac{240}{9^\text{x}}$
$9^\text{x}\times80=240$
$9^\text{x}=\frac{240}{80}$
$3^{2\text{x}}=3$
$3^{2\text{x}}=3^1$
By equating the exponents we get
$2\text{x}=1$
$\text{x}=\frac{1}{2}$
$\text{x}=0.5$
Hence the correct alternative is $a.$
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