Question
Solve for $\text{x}\Big(\frac{2}{5}\Big)^{2\text{x}-2}=\frac{32}{3125}.$
✓
Answer
$\text{x}\Big(\frac{2}{5}\Big)^{2\text{x}-2}=\frac{32}{3125}$
$\Rightarrow\Big(\frac{2}{5}\Big)^{2\text{x}-2}=\frac{2^5}{5^5}$
$\Rightarrow\Big(\frac{2}{5}\Big)^{2\text{x}-2}=\Big(\frac{2}{5}\Big)^5$
$\Rightarrow2\text{x}-2=5$
$\Rightarrow2\text{x}=7$
$\Rightarrow\text{x}=\frac{7}{2}$
$\Rightarrow\Big(\frac{2}{5}\Big)^{2\text{x}-2}=\frac{2^5}{5^5}$
$\Rightarrow\Big(\frac{2}{5}\Big)^{2\text{x}-2}=\Big(\frac{2}{5}\Big)^5$
$\Rightarrow2\text{x}-2=5$
$\Rightarrow2\text{x}=7$
$\Rightarrow\text{x}=\frac{7}{2}$
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