Question
Find the value of x for which $5^{2\text{x}}\div5^{3}=5^5.$
✓
Answer
$5^{2\text{x}}\div5^{3}=5^5$
$\Rightarrow5^{2\text{x}}\div5^5=5^{-3}$
$\Rightarrow5^{2\text{x}}=5^{5-3}=5^{2}$
Comparing, we get:
$2\text{x}=2\Rightarrow\text{x}=\frac{2}{2}=1$
$\therefore\text{x}=1$
$\Rightarrow5^{2\text{x}}\div5^5=5^{-3}$
$\Rightarrow5^{2\text{x}}=5^{5-3}=5^{2}$
Comparing, we get:
$2\text{x}=2\Rightarrow\text{x}=\frac{2}{2}=1$
$\therefore\text{x}=1$
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