Express log₁₀((x²y³)/z) in terms of log₁₀x, log₁₀y and log₁₀z.

Given, ⇒ log10 x2 y3 - log10 z ⇒ log10 x2 + log10 y3 - log10 z ⇒ 2 log10 x + 3 log10 y - log10 z. Hence, log10 = 2 log10 x + 3 log10 y - log10 z.

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Given,

$\log_{10} \space \Big(\dfrac{x^2y^3}{z}\Big)$

⇒ log₁₀ x² y³ - log₁₀ z

⇒ log₁₀ x² + log₁₀ y³ - log₁₀ z

⇒ 2 log₁₀ x + 3 log₁₀ y - log₁₀ z.

Hence, log₁₀ $\Big(\dfrac{x^2y^3}{z}\Big)$ = 2 log₁₀ x + 3 log₁₀ y - log₁₀ z.

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