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

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

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

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.

Simplify : log (a)³÷ log a

Express the following in terms of log 2 and log 3: log 648

Write the logarithmic equation for:

n = `sqrt(("M"."g")/("m".l)`

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If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: `"log" sqrt(72)`

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