Given log 10 a = b, express 10 2b - 3 in terms of a.

Given, ⇒ log 10 a = b ∴ a = 10 b . Simplifying 10 2b - 3 we get, ⇒ 10 2b - 3 = 10 2b .10 -3 = = . Hence, 10 2b - 3 =

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Mathematics

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Given,

⇒ log₁₀a = b

∴ a = 10^b.

Simplifying 10^{2b - 3} we get,

⇒ 10^{2b - 3} = 10^2b.10^-3

= $\dfrac{10^{2b}}{10^3} = \dfrac{(10^b)^2}{10^3}$

= $\dfrac{a^2}{10^3} = \dfrac{a^2}{1000}$ .

Hence, 10^{2b - 3} = $\dfrac{a^2}{1000}.$

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