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

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

Prove that:

log₁₀ 125 = 3(1 - log₁₀2).

Express the following in terms of log 2 and log 3: log 36

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

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

Write the logarithmic equation for:

E = `(1)/(2)"m v"^2`

Write the logarithmic equation for:

V = `(1)/("D"l) sqrt("T"/(pi"r")`

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

If log₁₀25 = x and log₁₀27 = y; evaluate without using logarithmic tables, in terms of x and y: log₁₀3

Simplify: log b ÷ log b²

Find the value of:

`("log"sqrt125 - "log"sqrt(27) - "log"sqrt(8))/("log"6 - "log"5)`