If $5^{3 x} = 125 a n d 10^{y} = 0.001 f i n d x a n d y .$

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Solution

$5^{3 x} = 125 a n d 10^{y} = 0.001 5^{3 x} = 125 = (5)^{3} ∴ 3 x = 3 \Rightarrow x = \frac{3}{3} = 1 a n d 10^{y} = 0.001 = \frac{1}{1000} = \frac{1}{10^{3}} = 10^{- 3} ∴ y = - 3 H e n c e, x = 1, y = - 3$

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