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

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: log₃ m = x and log₃ n = y.
Express 3^{2x - 3} in terms of m.

Express the following in terms of log 2 and log 3: log 36

Express the following in terms of log 2 and log 3: log 216

Express the following in terms of log 2 and log 3: `"log"root(5)(216)`

Express the following as a single logarithm:

`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log45

If log 4 = 0.6020, find the value of each of the following: log2.5

If log 8 = 0.90, find the value of each of the following: log4

If log 27 = 1.431, find the value of the following: log 9

Find the value of:

`("log"sqrt(8))/(8)`