Question
Solve : $3^{x-1}\times 5^{2y-3}= 225.$
✓
Answer
$ 3^{x-1} \times 5^{2 y-3}=225$
$ \Rightarrow 3^{x-1} \times 5^{2 y-3}=3^2 \times 5^2$
$ \Rightarrow x-1=2$ and $2 y-3=2$
$ \Rightarrow x=3$ and $2 y=5$
$ \Rightarrow x=3$ and $y=\frac{5}{2}$
$ \Rightarrow x=3$ and $y=2 \frac{1}{2}$
$ \Rightarrow 3^{x-1} \times 5^{2 y-3}=3^2 \times 5^2$
$ \Rightarrow x-1=2$ and $2 y-3=2$
$ \Rightarrow x=3$ and $2 y=5$
$ \Rightarrow x=3$ and $y=\frac{5}{2}$
$ \Rightarrow x=3$ and $y=2 \frac{1}{2}$
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