If Log 27 = 1.431, Find the Value of : Log 300 - Mathematics

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

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 300
= log( 3 x 100 )
= log 3 + log 100
= log 3 + 2 ...[ ∵ log₁₀100 = 2 ]
= 0.477 + 2
= 2.477

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 2.2 | Page 108

Given 3log x + `1/2`log y = 2, express y in term of x.

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

Given: log₃ m = x and log₃n = y.

Write down `3^(1 - 2y + 3x)` in terms of m and n.

Prove that:

log₁₀ 125 = 3(1 - log₁₀2).

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

Write the logarithmic equation for:

F = `"G"("m"_1"m"_2)/"d"^2`

Write the logarithmic equation for:

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

Express the following as a single logarithm:

`2"log"(9)/(5) - 3"log"(3)/(5) + "log"(16)/(20)`

Express the following as a single logarithm:

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

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