If $5^{3x} = 125$ and $10^y = 0.001$ find $x$ and $y$.
Given:
$5^{3x} = 125$ and $10^y = 0.001$
To do:
We have to find the values of $x$ and $y$.
Solution:
We know that,
$(a^{m})^{n}=a^{m n}$
$a^{m} \times a^{n}=a^{m+n}$
$a^{m} \div a^{n}=a^{m-n}$
$a^{0}=1$
Therefore,
$5^{3 x}=125$
$=(5)^{3}$
Comparing both sides, we get,
$3 x=3$
$\Rightarrow x=1$
$10^{y}=0.001$
$=\frac{1}{1000}$
$=\frac{1}{10^{3}}$
$=10^{-3}$
Comparing both sides, we get,
$y=-3$
The values of $x$ and $y$ are $1$ and $-3$ respectively.
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