Question
Solve the following equations:
$3^{\text{x}-1}\times5^{2\text{y}-3}=225$
$3^{\text{x}-1}\times5^{2\text{y}-3}=225$
✓
Answer
$3^{\text{x}-1}\times5^{2\text{y}-3}=225$
$\Rightarrow3^{\text{x}-1}\times5^{2\text{y}-3}=9\times25$
$\Rightarrow3^{\text{x}-1}\times^{2\text{y}-3}=3^2\times5^2$
$\Rightarrow\text{x}-1=2$ and $2\text{y}=3=2$
$\Rightarrow\text{x}=3$ and $\text{y}=\frac{5}{2}$
$\Rightarrow3^{\text{x}-1}\times5^{2\text{y}-3}=9\times25$
$\Rightarrow3^{\text{x}-1}\times^{2\text{y}-3}=3^2\times5^2$
$\Rightarrow\text{x}-1=2$ and $2\text{y}=3=2$
$\Rightarrow\text{x}=3$ and $\text{y}=\frac{5}{2}$
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