If Log 27 = 1.431, Find the Value of : Log 9

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

Sum

log 27 = 1.431
⇒ log 3 x 3 x 3 = 1.431
⇒ log 3³ = 1.431
⇒ 3log3 = 1.431
⇒ log 3 = `1.431/3`
⇒ log 3 = 0.477 ...(1)

log 9
= log( 3 x 3 )
= log 32
= 2 log 3
= 2 x 0.477 ...[ from(1) ]
= 0.954

shaalaa.com

Expansion of Expressions with the Help of Laws of Logarithm

Is there an error in this question or solution?

Chapter 8: Logarithms - Exercise 8 (C) [Page 108]

Chapter 8 Logarithms
Exercise 8 (C) | Q 2.1 | Page 108

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

Given: log₃ m = x and log₃ n = y.
Express 3^{2x - 3} in terms of m.

Prove that:

log₁₀ 125 = 3(1 - log₁₀2).

Express the following in terms of log 2 and log 3: log 216

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

Express the following in terms of log 2 and log 3: `"log"(26)/(51) - "log"(91)/(119)`

Express the following as a single logarithm:

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

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 75

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