If Log1025 = X and Log1027 = Y; Evaluate Without Using Logarithmic Tables, in Terms of X and Y: Log103

If log₁₀25 = x and log₁₀27 = y; evaluate without using logarithmic tables, in terms of x and y: log₁₀3

Sum

log₁₀27 = y
⇒ log₁₀3³ = y
⇒ 3log₁₀3 = y
⇒ log₁₀3 = `y/(3)`.

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Expansion of Expressions with the Help of Laws of Logarithm

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Chapter 10: Logarithms - Exercise 10.2

Chapter 10 Logarithms
Exercise 10.2 | Q 18.2

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

Given: log₃ m = x and log₃ n = y.
If 2 log₃ A = 5x - 3y; find A in terms of m and n.

Express the following in terms of log 2 and log 3: log12⁸

Express the following in terms of log 5 and/or log 2: log500

Express the following as a single logarithm:

`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`

Express the following as a single logarithm:

`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 720

If log x = p + q and log y = p - q, find the value of log `(10x)/y^2` in terms of p and q.

If 2 log y - log x - 3 = 0, express x in terms of y.

If log 4 = 0.6020, find the value of each of the following: log8