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

योग

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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अध्याय 10: Logarithms - Exercise 10.2

अध्याय 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: `"log" root(3)(144)`

Express the following as a single logarithm:
log 18 + log 25 - log 30

Simplify the following:

`2 "log" 5 +"log" 8 - (1)/(2) "log" 4`

Simplify the following:

`3"log" (32)/(27) + 5 "log"(125)/(24) - 3"log" (625)/(243) + "log" (2)/(75)`

If log x = p + q and log y = p - q, find the value of log `(10x)/y^2` in terms of p and q.

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

If log 8 = 0.90, find the value of each of the following: `"log"sqrt(32)`

If log 27 = 1.431, find the value of the following: log 9