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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Updated on: 10-Oct-2022

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