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

बेरीज

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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पाठ 10: Logarithms - Exercise 10.2

पाठ 10 Logarithms
Exercise 10.2 | Q 18.2

If log 2 = 0.3010 and log 3 = 0.4771 ; find the value of : log 1.2

Prove that : (log a)² - (log b)² = log `(( a )/( b ))` . Log (ab)

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

If log (a + 1) = log (4a - 3) - log 3; find a.

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

Express the following as a single logarithm:
log 18 + log 25 - log 30

Express the following as a single logarithm:
log 144 - log 72 + log 150 - log 50

Simplify the following:

`3"log" (32)/(27) + 5 "log"(125)/(24) - 3"log" (625)/(243) + "log" (2)/(75)`

If 2 log x + 1 = 40, find: x

If x² + y² = 6xy, prove that `"log"((x - y)/2) = (1)/(2)` (log x + log y)