If Log10 a = B, Find 103b - 2 in Terms of A.

If log₁₀ a = b, find 10^{3b - 2} in terms of a.

Sum

log₁₀ a = b
⇒ 10^b = a

⇒ ( 10^b )³ = a³ ...[ Cubing both sides ]

⇒ `10^(3b)/10^2 = a^3/10^2` ...[dividing both sides by 10²]

⇒ 10^{3b - 2}= `a^3/100`

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Expansion of Expressions with the Help of Laws of Logarithm

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Chapter 8: Logarithms - Exercise 8 (C) [Page 108]

Chapter 8 Logarithms
Exercise 8 (C) | Q 3 | Page 108

Given 2 log₁₀ x + 1 = log₁₀ 250, find :
(i) x
(ii) log₁₀ 2x

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