Express the Following in Terms of Log 2 and Log 3: Log 144

Express the following in terms of log 2 and log 3: log 144

Sum

log 144
= log (2⁴ x 3²)
= log 2⁴ + log3²
= 4 log 2 + 2 log 3.

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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 1.3

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

If log₁₀ a = b, find 10^{3b - 2} in terms of a.

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

Express the following in terms of log 5 and/or log 2: log160

Express the following as a single logarithm:

`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 12

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

If log 4 = 0.6020, find the value of each of the following: log8

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

Find the value of:

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