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

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

If log (a + b) = log a + log b, find a in terms of b.

If log₁₀ 8 = 0.90; find the value of : log√32

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

Simplify the following:

`2"log" 7 + 3 "log" 5 - "log"(49)/(8)`

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 720

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log45

If 2 log y - log x - 3 = 0, express x in terms of y.

If log 4 = 0.6020, find the value of each of the following: log2.5

If x² + y² = 7xy, prove that `"log"((x - y)/3) = (1)/(2)` (log x + log y)

Find the value of:

`("log"sqrt(8))/(8)`