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 7: Logarithms - Exercise 10.2

Chapter 7 Logarithms
Exercise 10.2 | Q 18.2

If log₅ x = y, find 5^{2y+ 3} in terms of x.

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

Express the following in terms of log 5 and/or log 2: log250

Express the following in terms of log 2 and log 3: `"log" root(4)(648)`

Express the following as a single logarithm:

`2 + 1/2 "log" 9 - 2 "log" 5`

Express the following as a single logarithm:

`(1)/(2)"log"25 - 2"log"3 + "log"36`

If log a = p and log b = q, express `"a"^3/"b"^2` in terms of p and q.

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

If log 2 = x and log 3 = y, find the value of each of the following on terms of x and y: log1.2

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