If Log 27 = 1.431, Find the Value of the Following: Log300

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

Sum

log 27
= log 3³
= 3 log 3
= 1.431
⇒ log 3
= `(1.431)/(3)`
= 0.477
∴ log300
= log(3 x 100)
= log(3 x 10²)
= log3 + 2 log 10
= 0.477 + 2
= 2.477.

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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 24.2

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

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

Prove that:

log₁₀ 125 = 3(1 - log₁₀2).

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

Express the following in terms of log 2 and log 3: `"log" root(4)(648)`

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

Express the following as a single logarithm:

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

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: log₁₀3

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log18