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Mathematics

If 53x = 125 and (10)y = 0.001, find x and y.

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Answer

Given,

⇒ 53x = 125

⇒ 53x = 53

⇒ 3x = 3

⇒ x = 1.

Given,

⇒10y=0.001⇒10y=11000⇒10y=1103⇒10y=10−3⇒y=−3.\Rightarrow 10^y = 0.001 \\[1em] \Rightarrow 10^y = \dfrac{1}{1000} \\[1em] \Rightarrow 10^y = \dfrac{1}{10^3} \\[1em] \Rightarrow 10^y = 10^{-3} \\[1em] \Rightarrow y = -3.

Hence, x = 1 and y = -3.

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