If Log1025 = X and Log1027 = Y; Evaluate Without Using Logarithmic Tables, in Terms of X and Y: Log105

If log₁₀25 = x and log₁₀27 = y; evaluate without using logarithmic tables, in terms of x and y: log₁₀5

Sum

log₁₀25 = x
⇒ log₁₀5² =x
⇒ 2log₁₀5 = x
⇒ log₁₀5 = `x/(2)`.

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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 18.1

If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 15

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

If log 27 = 1.431, find the value of : log 300

Simplify : log (a)³÷ log a

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

Express the following as a single logarithm:

`2"log"(15)/(18) - "log"(25)/(162) + "log"(4)/(9)`

Express the following as a single logarithm:

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

Express the following as a single logarithm:

`3"log"(5)/(8) + 2"log"(8)/(15) - (1)/(2)"log"(25)/(81) + 3`

Simplify the following:

`12"log" (3)/(2) + 7 "log" (125)/(27) - 5 "log" (25)/(36) - 7 "log" 25 + "log" (16)/(3)`

If log 27 = 1.431, find the value of the following: log300